Prosecution Insights
Last updated: July 17, 2026
Application No. 18/649,951

BAYESIAN METHOD AND SYSTEM FOR ESTIMATING KEY AGRICULTURAL FIELD MANAGEMENT PRACTICES

Non-Final OA §103§112§DOUBLEPATENT
Filed
Apr 29, 2024
Priority
Apr 28, 2023 — provisional 63/462,861
Examiner
MEINECKE DIAZ, SUSANNA M
Art Unit
3625
Tech Center
3600 — Transportation & Electronic Commerce
Assignee
Cibo Technologies Inc.
OA Round
3 (Non-Final)
31%
Grant Probability
At Risk
3-4
OA Rounds
2y 1m
Est. Remaining
51%
With Interview

Examiner Intelligence

Grants only 31% of cases
31%
Career Allowance Rate
213 granted / 695 resolved
-21.4% vs TC avg
Strong +20% interview lift
Without
With
+20.5%
Interview Lift
resolved cases with interview
Typical timeline
4y 3m
Avg Prosecution
44 currently pending
Career history
747
Total Applications
across all art units

Statute-Specific Performance

§101
17.0%
-23.0% vs TC avg
§103
56.1%
+16.1% vs TC avg
§102
8.7%
-31.3% vs TC avg
§112
5.8%
-34.2% vs TC avg
Black line = Tech Center average estimate • Based on career data from 695 resolved cases

Office Action

§103 §112 §DOUBLEPATENT
DETAILED ACTION Continued Examination Under 37 CFR 1.114 A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this application is eligible for continued examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on March 24, 2026 has been entered. Claims 1-3, 8-10, and 15-17 have been amended. Claims 1-20 are presented for examination. Notice of Pre-AIA or AIA Status The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . Response to Arguments Applicant's arguments filed March 24, 2026 have been fully considered but they are not persuasive. Applicant has requested that the Double Patenting rejections be held in abeyance until patentable subject matter is identified (page 14 of Applicant’s response). This request is granted. Regarding the rejections under 35 U.S.C. § 103, Applicant makes assertions as to what is and is not taught by each reference individually (pages 14-16 of Applicant’s response); however, Applicant has not addressed the obviousness rendered by the combination of the teachings and suggestions of the references collectively. Additionally, the Examiner has introduced the Jiang reference into the rejections in order to help address some of the claim amendments. Claim Rejections - 35 USC § 112 The following is a quotation of the first paragraph of 35 U.S.C. 112(a): (a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention. The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112: The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention. Claims 1-20 are rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention. Independent claims 1, 8, and 15 have been amended to recite: constructing hierarchical prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages; and performing probabilistic inference over the phenological parameter sets within the hierarchical prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date. Applicant’s original disclosure does not mention “hierarchical” or any variation thereof or synonyms (like tier, level, or layer in the corresponding context), much less in terms of the prior distributions of the Bayesian crop model being “hierarchical.” Therefore, these limitations present new matter. The dependent claims inherit this rejection. Claim Rejections - 35 USC § 103 The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action: A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made. Claims 1, 2, 4, 5, 8, 9, 11, 12, 15, 16, and 18 are rejected under 35 U.S.C. 103 as being unpatentable over Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Allan et al. (US 2020/0258205) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.). [Claim 1] Elkin discloses a computer-implemented method for predicting agricultural management practices (abstract), the method comprising: generating a training dataset that comprises a plurality of years of known management practices associated with a plurality of fields dispersed within geographic region along with a corresponding plurality of years of first remote sense images (¶¶ 33, 39, 52, 63, 75, 77 – One or more fields in an area; ¶ 34 – “The seasonal image data herein refer to data with the characteristic of a time series in which the data experiences regular and predictable changes that recur every calendar year. Seasonal image data comprises one or more images or data representations of said one or more images. The raw season image data obtained externally may be processed or pre-processed. The processed season image data may be used as training data for training one or more crop models of the Bayesian framework.”; ¶ 97 – “Examples of these ML methods or techniques may include or be based on, by way of example only but is not limited to, one or more of: any ML technique or algorithm/method that can be used to generate a trained model based on a labelled and/or unlabeled training datasets… Bayesian networks…”; ¶ 111 – “As an option, each crop model is trained using a labelled training dataset comprising historical planting information annotated with respect to at least one crop from said at least one agricultural field.”); training a Bayesian crop model to predict the plurality of years of known management practices associated with the plurality of fields using the corresponding plurality of years of first remote sense images as inputs (¶ 34 – “The seasonal image data herein refer to data with the characteristic of a time series in which the data experiences regular and predictable changes that recur every calendar year. Seasonal image data comprises one or more images or data representations of said one or more images. The raw season image data obtained externally may be processed or pre-processed. The processed season image data may be used as training data for training one or more crop models of the Bayesian framework.”; ¶ 97 – “Examples of these ML methods or techniques may include or be based on, by way of example only but is not limited to, one or more of: any ML technique or algorithm/method that can be used to generate a trained model based on a labelled and/or unlabeled training datasets… Bayesian networks…”; ¶ 111 – “As an option, each crop model is trained using a labelled training dataset comprising historical planting information annotated with respect to at least one crop from said at least one agricultural field.”); providing a time series of second remote sense images associated with a corresponding field having unknown management practices as exclusive inputs to the Bayesian crop model (¶ 34 – “The seasonal image data herein refer to data with the characteristic of a time series in which the data experiences regular and predictable changes that recur every calendar year. Seasonal image data comprises one or more images or data representations of said one or more images. The raw season image data obtained externally may be processed or pre-processed. The processed season image data may be used as training data for training one or more crop models of the Bayesian framework.”; ¶ 35 – “The seasonal image data for an agricultural field retains certain information on or about the particular crop or species of the crop, which may be used to infer crop states. Historical agricultural data with respect to the same will retain the same or similar information, which corresponds to the seasonal image data in some manner, whether it is for a planting date, classification, harvest, yield, or any other crop state described herein.”; ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 87, 89 – Satellite image data may continuously be used, via a Bayesian framework, to infer and predict crop-related information.); and executing the Bayesian crop model to predict a crop type, a planting date, and emergence date, and a harvest date for the corresponding field ( [0109] As an option, said one or more crop models comprise at least one base model conditioned on at least two crop stages in a previous agricultural season. As an option, said at least one base model is trained using annotated historical common land unit data, in order to predict said at least two crop states in an agricultural season following the previous agricultural season. As an option, said at least two crop states in the agricultural season are calculated at least in part from said seasonal image data. As an option, said at least one base model is configured to generate the forecast of said at least one crop state based on said seasonal image data. As an option, each crop state is a crop type, a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest date, or a damage to crop. As an option, the seasonal image data is processed with respect to each pixel of an image corresponding to a crop planted in said at least one agricultural field. [0110] As an option, further comprising: configuring the Bayesian framework to model a crop state in a previous agricultural season using seasonal image data of the previous agricultural season; and recalibrating said one or more probabilities based on the configured Bayesian framework, wherein said one or more probabilities are adapted to outputs of said one or more crop models. As an option, the Bayesian framework is configured to: classify, based on a crop type, at least one crop from at least one subset of the seasonal image data; determine said one or more probabilities for each classified crop; and update the Bayesian framework based on the classification in relation to said one or more probabilities. As an option, said one or more crop models comprises crop planting date prediction model, crop yield prediction model, crop acreage model, cover crop model, crop emergence date model, crop harvest model, and crop damage model. As an option, each crop model is configured to generate, based on said one or more probabilities, a crop state prediction associated with said at least one agricultural field in relation to the seasonal image data from at least one agricultural season.), the executing comprising: treating the estimated first associated posterior distribution parameters as known quantities (¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”); and using the known quantities to generate the crop type, the planting date, the emergence date, and the harvest date from estimated second associated posterior distribution parameters derived from the time series of second remote sense images (¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110). Elkin does not explicitly disclose: the training [of a Bayesian crop model] comprising: cleansing the corresponding plurality of years of remote sense images by: removing images with first missing data below a prescribed threshold; retaining images with second missing data above the prescribed threshold; time-processing third data from other time-adjacent images that corresponds to the second missing data; and using the time-processing third data to replace the second missing data; combining spectral band images for each observation data to generate corresponding first composite images; combining first composite images for each observation date to create composite estimated growth curves for each of the plurality of fields. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Regarding the use of time-series remote sensing, Zhang states: “The classifier based on a single-date image was first used for land cover classification. But the different landcover with the same spectrum at a given period limits the classification accuracy. To overcome this problem, classification based on time-series remote sensing has been proposed. Compared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Zhang further acknowledges that “the abnormal lower value in time series, led by cloud or shade, can be rebuilt by the value of adjacent time.” (Zhang: p. 632: section 2.2.3) Zhang states, “Improvements in the classification method, such as the development of machine learning (ML)(Wang et al. 2020a; Yu et al. 2020) and deep learning (DL) (Li et al. 2017, 2020; Liu et al. 2020a; Liu,Yang, and Lunga 2021; Xu et al. 2021), have enabled to capture sufficient characteristics from time-series images.” (Zhang: p. 627: section 1) The time series may reveal spectral changes (Zhang: p. 627: section 1 – “In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020)”) and Zhang references use of a Multi-Spectral Imager (MSI) on Sentinel-2 and Operational Land Imager (OPI) on Landsat-8 (Zhang: p. 630: section 2.2.1). In other words, Zhang recognizes that satellite imaging accuracy may be a problem due to cloud cover and that adjacent time values in the time series may be used to compensate, as needed. Zhang also recognizes that satellite images may include spectral band images. Zhang also discusses the use of double-sigmoid functions to analyze distributions related to crop growth, including the evaluation of a normalized difference vegetable index (NDVI) in relation to time/day and/or temperature (Zhang: pp. 634-636: section 2.3.2, including figures 5, 6). As to the cleansing of images and creation of composite images, as discussed above, Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitors change in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the Elkin-Zhang combination to perform the steps of the training [of a Bayesian crop model] comprising: cleansing the corresponding plurality of years of remote sense images by: removing images with first missing data below a prescribed threshold; retaining images with second missing data above the prescribed threshold; time-processing third data from other time-adjacent images that corresponds to the second missing data; and using the time-processing third data to replace the second missing data; combining spectral band images for each observation data to generate corresponding first composite images; combining first composite images for each observation date to create composite estimated growth curves for each of the plurality of fields in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). Elkin uses the known quantities to generate the crop type, the planting date, the emergence date, and the harvest date from estimated second associated posterior distribution parameters derived from the time series of second remote sense images (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110). Elkin does not explicitly disclose: employing generative Bayesian inference techniques that match the composite estimated growth curves to corresponding known crop vegetation index double-sigmoid functions to estimate first associated posterior distribution parameters; fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin to perform the steps of: employing generative Bayesian inference techniques that match the composite estimated growth curves to corresponding known crop vegetation index double-sigmoid functio ns to estimate first associated posterior distribution parameters; fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Elkin discloses: constructing prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages (¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 65 – “The update may be constrained by the weighted confidence predictions of each crop model.”); and performing probabilistic inference over the phenological parameter sets within the prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110; ¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 54 – “Each crop model may further comprise a base model conditioned on at least two crop states in a previous agricultural season. The base model is representative of a prior probability distribution used for predicting the state of the crop in the subsequent agricultural season or in the next iteration of recalibrating the same or additional crop models.”). Elkin does not explicitly disclose that the prior distributions of the Bayesian crop model are hierarchical. Jiang states, “The objective of this analysis was to apply a spatial Bayesian hierarchical model to examine the effects of soil, topographic and climate variables on corn yield.” (Jiang: p. 111: abstract) Relationships based on prior distributions and posterior distributions are evaluated (Jiang: p. 113). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin such that the prior distributions of the Bayesian crop model are hierarchical in order to reap the benefits of a Bayesian hierarchical approach to agricultural management, as explained in the following paragraph from pages 123-124 of Jiang: PNG media_image1.png 182 482 media_image1.png Greyscale PNG media_image2.png 128 478 media_image2.png Greyscale [Claim 8] Claim 8 recites limitations already addressed by the rejection of claim 1 above; therefore, the same rejection applies. Furthermore, Elkin discloses a non-transitory computer-readable storage medium storing instructions that, when executed by a computer, cause the computer to perform a method for predicting agricultural management practices (Elkin: ¶¶ 10-14). [Claim 15] Claim 15 recites limitations already addressed by the rejection of claim 1 above; therefore, the same rejection applies. Furthermore, Elkin discloses a system for predicting agricultural management practices, the system comprising an incentive program server, the server comprising a crop model processor, comprising a Bayesian crop model; a training processor; and a remote sense processor to perform its disclosed operations (Elkin: ¶¶ 10-14, 67, 96, 102-103). [Claims 2, 9, 16] Elkin does not explicitly disclose wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets. Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The purpose of filling in gaps in a series of time-based data is to provide temporal continuity. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the Elkin-Zhang combination wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). [Claims 4, 11, 18] Elkin does not explicitly disclose wherein the geographic region comprises the United States Corn Belt. Zhang explains the following: As one of the most important corn and soybean producers, the USA produces one-third of the world’s corn production. Most of the corn is planted in a belt region, which extends across 12 Midwest states and is called Corn Belt (Panagopoulos et al. 2015). Due to the influences of climate, cost of inputs, cropping patterns, and other factors, the cropping area changes every year, alternating planting corn and soybean. The corn cropping area could extend to the northwest of the USA (Green et al. 2018). This could lead to historic carbon losses, and no-till practices could help restore the lost soil organic carbon (Mishra, Ussiri, and Lal 2010; d’Andrimont et al. 2020). Insecticide applications may cause environmental pollution (Hladik, Kolpin, and Kuivila 2014). Therefore, it is important to develop a method to detect corn area change for agricultural management and environmental protection. (Zhang: p. 626) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin wherein the geographic region comprises the United States Corn Belt in order to facilitate the focus of analysis on geographical areas largely reliant on for a significant portion of the world’s food production, thereby ensuring sufficient food supplies. [Claims 5, 12] Elkin does not explicitly disclose wherein the geographic region comprises a state within the United States. Zhang explains the following: As one of the most important corn and soybean producers, the USA produces one-third of the world’s corn production. Most of the corn is planted in a belt region, which extends across 12 Midwest states and is called Corn Belt (Panagopoulos et al. 2015). Due to the influences of climate, cost of inputs, cropping patterns, and other factors, the cropping area changes every year, alternating planting corn and soybean. The corn cropping area could extend to the northwest of the USA (Green et al. 2018). This could lead to historic carbon losses, and no-till practices could help restore the lost soil organic carbon (Mishra, Ussiri, and Lal 2010; d’Andrimont et al. 2020). Insecticide applications may cause environmental pollution (Hladik, Kolpin, and Kuivila 2014). Therefore, it is important to develop a method to detect corn area change for agricultural management and environmental protection. (Zhang: p. 626) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin wherein the geographic region comprises a state within the United States in order to facilitate the focus of analysis on geographical areas largely reliant on for a significant portion of the world’s food production, thereby ensuring sufficient food supplies. Claims 3, 10, and 17 are rejected under 35 U.S.C. 103 as being unpatentable over Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Allan et al. (US 2020/0258205) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.), as applied to claims 1, 2, 8, 9, 15, and 16 above, in view of Richt (US 2018/0075546). [Claims 3, 10, 17] Elkin discloses wherein the Bayesian crop model approximates a posterior distribution of parameters (Elkin: ¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”). Elkin does not explicitly disclose that the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Zhang does not explicitly disclose “using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution.” In an agronomic environment, Richt describes the benefit of using Hamiltonian Markov chain Monte Carlo (MCMC) as follows: “[0197] Values for agronomic inputs for a farmable region can be determined using different metaheuristic techniques, such as a Markov chain Monte Carlo (MCMC) and approximate Bayesian computations or Simulated Annealing. Other metaheuristics can include genetic algorithms, differential evolution, particle swarm optimization, ant colony algorithms, tabu search, stochastic gradient ascent/descent, simultaneous perturbation stochastic approximation (SPSA), Differential Evolution Adaptive Metropolis (DREAM), and Hamiltonian MCMC. These methods enable the solution of optimization problems in large dimensional spaces.” The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin wherein the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and in order to “enable the solution of optimization problems in large dimensional spaces” (Richt: ¶ 197). Claims 6, 7, 13, 14, 19, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Allan et al. (US 2020/0258205) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.), as applied to claims 1, 8, and 15 above, in view of Perry et al. (US 2019/0050948). [Claims 6, 13, 19] Elkin discloses wherein the crop type, the planting date, the emergence date, and the harvest date are employed (Elkin: ¶¶ 34-38, 40-41); however, Elkin does not explicitly disclose wherein the crop type, the planting date, the emergence date, and the harvest date are employed to prepopulate an enrollment application for participation of the field in a grower incentive program. Perry describes an automated system for generating crop acquisition agreements (Perry: ¶ 38 – “Thus, the user of the broker client device may be a crop recipient. In one embodiment, the broker client device 104 accesses the crop prediction system 125 via an interface 130 generated by the crop prediction system 125 that allows the user of the broker client device 104 to identify predicted crop production information from one or more growers, to identify sets of farming operations to suggest or provide to the one or more growers in order to optimize crop production, to identify one or more prospective crop recipients in addition to the crop broker, and to automate the generation of crop acquisition agreements with the one or more prospective crop recipients. A crop recipient may receive a harvested crop from a grower or from a crop broker.”). Selling a crop to a crop recipient provides an incentive to a crop grower and/or broker. Like Elkin, Perry predicts crop characteristics (Perry: ¶ 119 – “In some embodiments, the training module 410 can update a crop prediction model responsive to an agricultural event (e.g., a planted crop achieves a plant growth stage, such as germination, flowering, and the like). Likewise, the training module 410 can update a crop prediction model response to a request received by the crop prediction engine 155 (e.g., by a grower or an agronomist). In some embodiments, the training module 410 updates the crop prediction models iteratively, such that a crop prediction output from a crop prediction model is incorporated into a training set of data used to train crop prediction models. For example, if a prediction model generates a set of farming operations identifying a crop variant to plant and a planting date range to optimize crop production, the training module 410 can incorporate the set of farming operations into a training set for use in training or retraining crop prediction models.”). The crop broker and crop recipient may be provided with crop prediction information via their respective client devices (Perry: ¶ 79). The crop broker and crop recipient can use the provided information to enter into contractual agreements with more confidence in light of reduced risk due to the crop prediction information (as suggested in ¶¶ 188-202 of Perry). Selling a crop to a crop recipient provides an incentive to a crop grower and/or broker. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin wherein the crop type, the planting date, the emergence date, and the harvest date are employed to prepopulate an enrollment application for participation of the field in a grower incentive program in order to provide additional confidence in crop predictions, thereby reducing the risk of creating crop acquisition agreements among parties (as suggested in ¶¶ 188-202 of Perry). [Claims 7, 14, 20] Elkin discloses wherein the crop type, the planting date, the emergence date, and the harvest date are employed (Elkin: ¶¶ 34-38, 40-41); however, Elkin does not explicitly disclose wherein the crop type, the planting date, the emergence date, and the harvest date are employed to verify implementation of incentive program management practices corresponding to participation of the field a grower incentive program. Perry describes an automated system for generating crop acquisition agreements (Perry: ¶ 38 – “Thus, the user of the broker client device may be a crop recipient. In one embodiment, the broker client device 104 accesses the crop prediction system 125 via an interface 130 generated by the crop prediction system 125 that allows the user of the broker client device 104 to identify predicted crop production information from one or more growers, to identify sets of farming operations to suggest or provide to the one or more growers in order to optimize crop production, to identify one or more prospective crop recipients in addition to the crop broker, and to automate the generation of crop acquisition agreements with the one or more prospective crop recipients. A crop recipient may receive a harvested crop from a grower or from a crop broker.”). Selling a crop to a crop recipient provides an incentive to a crop grower and/or broker. Like Elkin, Perry predicts crop characteristics (Perry: ¶ 119 – “In some embodiments, the training module 410 can update a crop prediction model responsive to an agricultural event (e.g., a planted crop achieves a plant growth stage, such as germination, flowering, and the like). Likewise, the training module 410 can update a crop prediction model response to a request received by the crop prediction engine 155 (e.g., by a grower or an agronomist). In some embodiments, the training module 410 updates the crop prediction models iteratively, such that a crop prediction output from a crop prediction model is incorporated into a training set of data used to train crop prediction models. For example, if a prediction model generates a set of farming operations identifying a crop variant to plant and a planting date range to optimize crop production, the training module 410 can incorporate the set of farming operations into a training set for use in training or retraining crop prediction models.”). The crop broker and crop recipient may be provided with crop prediction information via their respective client devices (Perry: ¶ 79). The crop broker and crop recipient can use the provided information to enter into contractual agreements with more confidence in light of reduced risk due to the crop prediction information (as suggested in ¶¶ 188-202 of Perry). Selling a crop to a crop recipient provides an incentive to a crop grower and/or broker. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify Elkin wherein the crop type, the planting date, the emergence date, and the harvest date are employed to verify implementation of incentive program management practices corresponding to participation of the field a grower incentive program in order to provide additional confidence in crop predictions, thereby reducing the risk of creating crop acquisition agreements among parties (as suggested in ¶¶ 188-202 of Perry). Double Patenting The nonstatutory double patenting rejection is based on a judicially created doctrine grounded in public policy (a policy reflected in the statute) so as to prevent the unjustified or improper timewise extension of the “right to exclude” granted by a patent and to prevent possible harassment by multiple assignees. A nonstatutory double patenting rejection is appropriate where the conflicting claims are not identical, but at least one examined application claim is not patentably distinct from the reference claim(s) because the examined application claim is either anticipated by, or would have been obvious over, the reference claim(s). See, e.g., In re Berg, 140 F.3d 1428, 46 USPQ2d 1226 (Fed. Cir. 1998); In re Goodman, 11 F.3d 1046, 29 USPQ2d 2010 (Fed. Cir. 1993); In re Longi, 759 F.2d 887, 225 USPQ 645 (Fed. Cir. 1985); In re Van Ornum, 686 F.2d 937, 214 USPQ 761 (CCPA 1982); In re Vogel, 422 F.2d 438, 164 USPQ 619 (CCPA 1970); In re Thorington, 418 F.2d 528, 163 USPQ 644 (CCPA 1969). A timely filed terminal disclaimer in compliance with 37 CFR 1.321(c) or 1.321(d) may be used to overcome an actual or provisional rejection based on nonstatutory double patenting provided the reference application or patent either is shown to be commonly owned with the examined application, or claims an invention made as a result of activities undertaken within the scope of a joint research agreement. See MPEP § 717.02 for applications subject to examination under the first inventor to file provisions of the AIA as explained in MPEP § 2159. See MPEP § 2146 et seq. for applications not subject to examination under the first inventor to file provisions of the AIA . A terminal disclaimer must be signed in compliance with 37 CFR 1.321(b). The filing of a terminal disclaimer by itself is not a complete reply to a nonstatutory double patenting (NSDP) rejection. A complete reply requires that the terminal disclaimer be accompanied by a reply requesting reconsideration of the prior Office action. Even where the NSDP rejection is provisional the reply must be complete. See MPEP § 804, subsection I.B.1. For a reply to a non-final Office action, see 37 CFR 1.111(a). For a reply to final Office action, see 37 CFR 1.113(c). A request for reconsideration while not provided for in 37 CFR 1.113(c) may be filed after final for consideration. See MPEP §§ 706.07(e) and 714.13. The USPTO Internet website contains terminal disclaimer forms which may be used. Please visit www.uspto.gov/patent/patents-forms. The actual filing date of the application in which the form is filed determines what form (e.g., PTO/SB/25, PTO/SB/26, PTO/AIA /25, or PTO/AIA /26) should be used. A web-based eTerminal Disclaimer may be filled out completely online using web-screens. An eTerminal Disclaimer that meets all requirements is auto-processed and approved immediately upon submission. For more information about eTerminal Disclaimers, refer to www.uspto.gov/patents/apply/applying-online/eterminal-disclaimer. Claims 1-20 are provisionally rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-20 of copending Application No. 18/649,808 in view of Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.) (and additionally in view of Allan et al. (US 2020/0258205) for claims 2, 9, and 16 and in view of Richt (US 2018/0075546) for claims 3, 10, and 17). Although the claims at issue are not identical, they are not patentably distinct from each other because claims 1-20 in the instant application are verbatim the same as claims 1-20 in the copending application, respectively, with the exception of the following: (a) Independent claims 1, 8, and 15 of the instant application recite “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” while the corresponding limitation recited in independent claims 1, 8, and 15 of the copending application does not include the planting date, the emergence date, and the harvest date. In other words, the corresponding limitation of claims 1, 8, and 15 of the copending application simply recites “executing the Bayesian crop model to predict a crop type for the corresponding field.” (b) Dependent claims 6, 7, 13, 14, 19, and 20 of the instant application refer to “the crop type, the planting date, the emergence date, and the harvest date” while dependent claims 6, 7, 13, 14, 19, and 20 of the copending application simply refer to “the crop type.” Elkin et al. (US 2023/0316116) addresses the gaps between the claim sets in the two applications in its disclosure of the following: [0109] As an option, said one or more crop models comprise at least one base model conditioned on at least two crop stages in a previous agricultural season. As an option, said at least one base model is trained using annotated historical common land unit data, in order to predict said at least two crop states in an agricultural season following the previous agricultural season. As an option, said at least two crop states in the agricultural season are calculated at least in part from said seasonal image data. As an option, said at least one base model is configured to generate the forecast of said at least one crop state based on said seasonal image data. As an option, each crop state is a crop type, a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest date, or a damage to crop. As an option, the seasonal image data is processed with respect to each pixel of an image corresponding to a crop planted in said at least one agricultural field. [0110] As an option, further comprising: configuring the Bayesian framework to model a crop state in a previous agricultural season using seasonal image data of the previous agricultural season; and recalibrating said one or more probabilities based on the configured Bayesian framework, wherein said one or more probabilities are adapted to outputs of said one or more crop models. As an option, the Bayesian framework is configured to: classify, based on a crop type, at least one crop from at least one subset of the seasonal image data; determine said one or more probabilities for each classified crop; and update the Bayesian framework based on the classification in relation to said one or more probabilities. As an option, said one or more crop models comprises crop planting date prediction model, crop yield prediction model, crop acreage model, cover crop model, crop emergence date model, crop harvest model, and crop damage model. As an option, each crop model is configured to generate, based on said one or more probabilities, a crop state prediction associated with said at least one agricultural field in relation to the seasonal image data from at least one agricultural season. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1-20 of copending Application No. 18/649,808 to incorporate the operation of “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” (as recited in independent claims 1, 8, and 15 of the instant application, with further reference to “the crop type, the planting date, the emergence date, and the harvest date” being made in dependent claims 6, 7, 13, 14, 19, and 20 of the instant application) in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (c) Independent claims 1, 8, and 15 of the instant application recite the following limitations that are not recited in the claims of the related application: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables; constructing hierarchical prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages; and performing probabilistic inference over the phenological parameter sets within the hierarchical prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application to perform the step of: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Elkin discloses: constructing prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages (¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 65 – “The update may be constrained by the weighted confidence predictions of each crop model.”); and performing probabilistic inference over the phenological parameter sets within the prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110; ¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 54 – “Each crop model may further comprise a base model conditioned on at least two crop states in a previous agricultural season. The base model is representative of a prior probability distribution used for predicting the state of the crop in the subsequent agricultural season or in the next iteration of recalibrating the same or additional crop models.”). Elkin does not explicitly disclose that the prior distributions of the Bayesian crop model are hierarchical. Jiang states, “The objective of this analysis was to apply a spatial Bayesian hierarchical model to examine the effects of soil, topographic and climate variables on corn yield.” (Jiang: p. 111: abstract) Relationships based on prior distributions and posterior distributions are evaluated (Jiang: p. 113). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application such that the prior distributions of the Bayesian crop model are hierarchical in order to reap the benefits of a Bayesian hierarchical approach to agricultural management, as explained in the following paragraph from pages 123-124 of Jiang: PNG media_image1.png 182 482 media_image1.png Greyscale PNG media_image2.png 128 478 media_image2.png Greyscale Such modifications would have been further beneficial in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (d) Regarding claims 2, 9, and 16, the corresponding claims in the related application do not fully recite wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets. Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The purpose of filling in gaps in a series of time-based data is to provide temporal continuity. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). (e) Regarding claims 3, 10, and 17, the corresponding claims in the related application do not fully recite wherein the Bayesian crop model approximates a posterior distribution over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Elkin discloses wherein the Bayesian crop model approximates a posterior distribution of parameters (Elkin: ¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”). Elkin does not explicitly disclose that the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Zhang does not explicitly disclose “using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution.” In an agronomic environment, Richt describes the benefit of using Hamiltonian Markov chain Monte Carlo (MCMC) as follows: “[0197] Values for agronomic inputs for a farmable region can be determined using different metaheuristic techniques, such as a Markov chain Monte Carlo (MCMC) and approximate Bayesian computations or Simulated Annealing. Other metaheuristics can include genetic algorithms, differential evolution, particle swarm optimization, ant colony algorithms, tabu search, stochastic gradient ascent/descent, simultaneous perturbation stochastic approximation (SPSA), Differential Evolution Adaptive Metropolis (DREAM), and Hamiltonian MCMC. These methods enable the solution of optimization problems in large dimensional spaces.” The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and in order to “enable the solution of optimization problems in large dimensional spaces” (Richt: ¶ 197). (f) The related application recites some limitations not recited in the claims of the instant application. Elimination of an element or its functions is deemed to be obvious in light of prior art teachings of at least the recited element or its functions (see In re Karlson, 136 USPQ 184, 186; 311 F2d 581 (CCPA 1963)). This is a provisional nonstatutory double patenting rejection because the patentably indistinct claims have not in fact been patented. Claims 1-20 are provisionally rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-20 of copending Application No. 18/649,970 in view of Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.) (and additionally in view of Allan et al. (US 2020/0258205) for claims 2, 9, and 16 and in view of Richt (US 2018/0075546) for claims 3, 10, and 17). Although the claims at issue are not identical, they are not patentably distinct from each other because claims 1-20 in the instant application are verbatim the same as claims 1-20 in the copending application, respectively, with the exception of the following: (a) Independent claims 1, 8, and 15 of the instant application recite “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” while the corresponding limitation recited in independent claims 1, 8, and 15 of the copending application also includes a senescence start date as a predicted factor. (b) Dependent claims 6, 7, 13, 14, 19, and 20 of the instant application refer to “the crop type, the planting date, the emergence date, and the harvest date” while dependent claims 6, 7, 13, 14, 19, and 20 of the copending application additionally refer to “the senescence start date.” (c) Independent claims 1, 8, and 15 of the instant application recite the following limitations that are not recited in the claims of the related application: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables; constructing hierarchical prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages; and performing probabilistic inference over the phenological parameter sets within the hierarchical prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application to perform the step of: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Elkin discloses: constructing prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages (¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 65 – “The update may be constrained by the weighted confidence predictions of each crop model.”); and performing probabilistic inference over the phenological parameter sets within the prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110; ¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 54 – “Each crop model may further comprise a base model conditioned on at least two crop states in a previous agricultural season. The base model is representative of a prior probability distribution used for predicting the state of the crop in the subsequent agricultural season or in the next iteration of recalibrating the same or additional crop models.”). Elkin does not explicitly disclose that the prior distributions of the Bayesian crop model are hierarchical. Jiang states, “The objective of this analysis was to apply a spatial Bayesian hierarchical model to examine the effects of soil, topographic and climate variables on corn yield.” (Jiang: p. 111: abstract) Relationships based on prior distributions and posterior distributions are evaluated (Jiang: p. 113). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application such that the prior distributions of the Bayesian crop model are hierarchical in order to reap the benefits of a Bayesian hierarchical approach to agricultural management, as explained in the following paragraph from pages 123-124 of Jiang: PNG media_image1.png 182 482 media_image1.png Greyscale PNG media_image2.png 128 478 media_image2.png Greyscale Such modifications would have been further beneficial in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (d) Regarding claims 2, 9, and 16, the corresponding claims in the related application do not fully recite wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets. Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The purpose of filling in gaps in a series of time-based data is to provide temporal continuity. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). (e) Regarding claims 3, 10, and 17, the corresponding claims in the related application do not fully recite wherein the Bayesian crop model approximates a posterior distribution over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Elkin discloses wherein the Bayesian crop model approximates a posterior distribution of parameters (Elkin: ¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”). Elkin does not explicitly disclose that the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Zhang does not explicitly disclose “using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution.” In an agronomic environment, Richt describes the benefit of using Hamiltonian Markov chain Monte Carlo (MCMC) as follows: “[0197] Values for agronomic inputs for a farmable region can be determined using different metaheuristic techniques, such as a Markov chain Monte Carlo (MCMC) and approximate Bayesian computations or Simulated Annealing. Other metaheuristics can include genetic algorithms, differential evolution, particle swarm optimization, ant colony algorithms, tabu search, stochastic gradient ascent/descent, simultaneous perturbation stochastic approximation (SPSA), Differential Evolution Adaptive Metropolis (DREAM), and Hamiltonian MCMC. These methods enable the solution of optimization problems in large dimensional spaces.” The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and in order to “enable the solution of optimization problems in large dimensional spaces” (Richt: ¶ 197). (f) The related application recites some limitations not recited in the claims of the instant application. Elimination of an element or its functions is deemed to be obvious in light of prior art teachings of at least the recited element or its functions (see In re Karlson, 136 USPQ 184, 186; 311 F2d 581 (CCPA 1963)). This is a provisional nonstatutory double patenting rejection because the patentably indistinct claims have not in fact been patented. Claims 1-20 are provisionally rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-20 of copending Application No. 18/649,834 in view of Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.) (and additionally in view of Allan et al. (US 2020/0258205) for claims 2, 9, and 16 and in view of Richt (US 2018/0075546) for claims 3, 10, and 17). Although the claims at issue are not identical, they are not patentably distinct from each other because claims 1-20 in the instant application are verbatim the same as claims 1-20 in the copending application, respectively, with the exception of the following: (a) Independent claims 1, 8, and 15 of the instant application recite “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” while the corresponding limitation recited in independent claims 1, 8, and 15 of the copending application does not include the emergence date and the harvest date. In other words, the corresponding limitation of claims 1, 8, and 15 of the copending application simply recites “executing the Bayesian crop model to predict a crop type and a planting date for the corresponding field.” (b) Dependent claims 6, 7, 13, 14, 19, and 20 of the instant application refer to “the crop type, the planting date, the emergence date, and the harvest date” while dependent claims 6, 7, 13, 14, 19, and 20 of the copending application simply refer to “the crop type and the planting date.” Elkin et al. (US 2023/0316116) addresses the gaps between the claim sets in the two applications in its disclosure of the following: [0109] As an option, said one or more crop models comprise at least one base model conditioned on at least two crop stages in a previous agricultural season. As an option, said at least one base model is trained using annotated historical common land unit data, in order to predict said at least two crop states in an agricultural season following the previous agricultural season. As an option, said at least two crop states in the agricultural season are calculated at least in part from said seasonal image data. As an option, said at least one base model is configured to generate the forecast of said at least one crop state based on said seasonal image data. As an option, each crop state is a crop type, a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest date, or a damage to crop. As an option, the seasonal image data is processed with respect to each pixel of an image corresponding to a crop planted in said at least one agricultural field. [0110] As an option, further comprising: configuring the Bayesian framework to model a crop state in a previous agricultural season using seasonal image data of the previous agricultural season; and recalibrating said one or more probabilities based on the configured Bayesian framework, wherein said one or more probabilities are adapted to outputs of said one or more crop models. As an option, the Bayesian framework is configured to: classify, based on a crop type, at least one crop from at least one subset of the seasonal image data; determine said one or more probabilities for each classified crop; and update the Bayesian framework based on the classification in relation to said one or more probabilities. As an option, said one or more crop models comprises crop planting date prediction model, crop yield prediction model, crop acreage model, cover crop model, crop emergence date model, crop harvest model, and crop damage model. As an option, each crop model is configured to generate, based on said one or more probabilities, a crop state prediction associated with said at least one agricultural field in relation to the seasonal image data from at least one agricultural season. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1-20 of copending Application No. 18/649,834 to incorporate the operation of “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” (as recited in independent claims 1, 8, and 15 of the instant application, with further reference to “the crop type, the planting date, the emergence date, and the harvest date” being made in dependent claims 6, 7, 13, 14, 19, and 20 of the instant application) in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (c) While the independent claims in the related application do not recite the following in the independent claims, the independent claims in the instant application have been amended to recite the following limitations, which are cumulatively addressed by Elkin, Zhang, and Allan. Elkin discloses the executing comprising: treating the estimated first associated posterior distribution parameters as known quantities (¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”); and using the known quantities to generate the crop type, the planting date, the emergence date, and the harvest date from estimated second associated posterior distribution parameters derived from the time series of second remote sense images (¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1, 8, and 15 of copending Application No. 18/649,834 to incorporate the aforementioned limitations (as recited in independent claims 1, 8, and 15 of the instant application) in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). The claims in the related application do not explicitly recite: the training [of a Bayesian crop model] comprising: cleansing the corresponding plurality of years of remote sense images by: removing images with first missing data below a prescribed threshold; retaining images with second missing data above the prescribed threshold; time-processing third data from other time-adjacent images that corresponds to the second missing data; and using the time-processing third data to replace the second missing data; combining spectral band images for each observation data to generate corresponding first composite images; combining first composite images for each observation date to create composite estimated growth curves for each of the plurality of fields; and employing generative Bayesian inference techniques that match the composite estimated growth curves to corresponding known crop vegetation index double-sigmoid functions to estimate first associated posterior distribution parameters. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Regarding the use of time-series remote sensing, Zhang states: “The classifier based on a single-date image was first used for land cover classification. But the different landcover with the same spectrum at a given period limits the classification accuracy. To overcome this problem, classification based on time-series remote sensing has been proposed. Compared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Zhang further acknowledges that “the abnormal lower value in time series, led by cloud or shade, can be rebuilt by the value of adjacent time.” (Zhang: p. 632: section 2.2.3) Zhang states, “Improvements in the classification method, such as the development of machine learning (ML)(Wang et al. 2020a; Yu et al. 2020) and deep learning (DL) (Li et al. 2017, 2020; Liu et al. 2020a; Liu,Yang, and Lunga 2021; Xu et al. 2021), have enabled to capture sufficient characteristics from time-series images.” (Zhang: p. 627: section 1) The time series may reveal spectral changes (Zhang: p. 627: section 1 – “In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020)”) and Zhang references use of a Multi-Spectral Imager (MSI) on Sentinel-2 and Operational Land Imager (OPI) on Landsat-8 (Zhang: p. 630: section 2.2.1). In other words, Zhang recognizes that satellite imaging accuracy may be a problem due to cloud cover and that adjacent time values in the time series may be used to compensate, as needed. Zhang also recognizes that satellite images may include spectral band images. Zhang also discusses the use of double-sigmoid functions to analyze distributions related to crop growth, including the evaluation of a normalized difference vegetable index (NDVI) in relation to time/day and/or temperature (Zhang: pp. 634-636: section 2.3.2, including figures 5, 6). As to the cleansing of images and creation of composite images, as discussed above, Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1, 8, and 15 of copending Application No. 18/649,834 to incorporate the steps of the training [of a Bayesian crop model] comprising: cleansing the corresponding plurality of years of remote sense images by: removing images with first missing data below a prescribed threshold; retaining images with second missing data above the prescribed threshold; time-processing third data from other time-adjacent images that corresponds to the second missing data; and using the time-processing third data to replace the second missing data; combining spectral band images for each observation data to generate corresponding first composite images; combining first composite images for each observation date to create composite estimated growth curves for each of the plurality of fields in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). Regarding the use of double-sigmoid functions (recited in the independent claims of the instant application), the Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1, 8, and 15 of copending Application No. 18/649,834 to perform the step of employing generative Bayesian inference techniques that match the composite estimated growth curves to corresponding known crop vegetation index double-sigmoid functions to estimate first associated posterior distribution parameters. employing generative Bayesian inference techniques that match the composite estimated growth curves to corresponding known crop vegetation index double-sigmoid functions to estimate first associated posterior distribution parameters “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) (c) Independent claims 1, 8, and 15 of the instant application recite the following limitations that are not recited in the claims of the related application: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables; constructing hierarchical prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages; and performing probabilistic inference over the phenological parameter sets within the hierarchical prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application to perform the step of: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Elkin discloses: constructing prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages (¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 65 – “The update may be constrained by the weighted confidence predictions of each crop model.”); and performing probabilistic inference over the phenological parameter sets within the prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110; ¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 54 – “Each crop model may further comprise a base model conditioned on at least two crop states in a previous agricultural season. The base model is representative of a prior probability distribution used for predicting the state of the crop in the subsequent agricultural season or in the next iteration of recalibrating the same or additional crop models.”). Elkin does not explicitly disclose that the prior distributions of the Bayesian crop model are hierarchical. Jiang states, “The objective of this analysis was to apply a spatial Bayesian hierarchical model to examine the effects of soil, topographic and climate variables on corn yield.” (Jiang: p. 111: abstract) Relationships based on prior distributions and posterior distributions are evaluated (Jiang: p. 113). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application such that the prior distributions of the Bayesian crop model are hierarchical in order to reap the benefits of a Bayesian hierarchical approach to agricultural management, as explained in the following paragraph from pages 123-124 of Jiang: PNG media_image1.png 182 482 media_image1.png Greyscale PNG media_image2.png 128 478 media_image2.png Greyscale Such modifications would have been further beneficial in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (d) Regarding claims 2, 9, and 16, the corresponding claims in the related application do not fully recite wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets. Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The purpose of filling in gaps in a series of time-based data is to provide temporal continuity. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). (e) Regarding claims 3, 10, and 17, the corresponding claims in the related application do not fully recite wherein the Bayesian crop model approximates a posterior distribution over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Elkin discloses wherein the Bayesian crop model approximates a posterior distribution of parameters (Elkin: ¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”). Elkin does not explicitly disclose that the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Zhang does not explicitly disclose “using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution.” In an agronomic environment, Richt describes the benefit of using Hamiltonian Markov chain Monte Carlo (MCMC) as follows: “[0197] Values for agronomic inputs for a farmable region can be determined using different metaheuristic techniques, such as a Markov chain Monte Carlo (MCMC) and approximate Bayesian computations or Simulated Annealing. Other metaheuristics can include genetic algorithms, differential evolution, particle swarm optimization, ant colony algorithms, tabu search, stochastic gradient ascent/descent, simultaneous perturbation stochastic approximation (SPSA), Differential Evolution Adaptive Metropolis (DREAM), and Hamiltonian MCMC. These methods enable the solution of optimization problems in large dimensional spaces.” The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and in order to “enable the solution of optimization problems in large dimensional spaces” (Richt: ¶ 197). (f) The related application recites some limitations not recited in the claims of the instant application. Elimination of an element or its functions is deemed to be obvious in light of prior art teachings of at least the recited element or its functions (see In re Karlson, 136 USPQ 184, 186; 311 F2d 581 (CCPA 1963)). This is a provisional nonstatutory double patenting rejection because the patentably indistinct claims have not in fact been patented. Claims 1-20 are provisionally rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-20 of copending Application No. 18/649,935 in view of Elkin et al. (US 2023/0316116) in view of Zhang et al. (Zhang, Lifu et al. (2022) "Crop Classification Based on the Spectrotemporal Signature Derived from Vegetation Indices and Accumulated Temperature," International Journal of Digital Earth, 15:1, 626-652) in view of Jiang et al. (Jiang, Pingping et al. "Bayesian Analysis of Within-Field Variability of Corn Yield Using a Spatial Hierarchical Model." Precision Agric (2009) 10:111-127. Published online: 9 July 2008.) (and additionally in view of Allan et al. (US 2020/0258205) for claims 2, 9, and 16 and in view of Richt (US 2018/0075546) for claims 3, 10, and 17). Although the claims at issue are not identical, they are not patentably distinct from each other because claims 1-20 in the instant application are verbatim the same as claims 1-20 in the copending application, respectively, with the exception of the following: (a) Independent claims 1, 8, and 15 of the instant application recite “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” while the corresponding limitation recited in independent claims 1, 8, and 15 of the copending application does not include the emergence date. In other words, the corresponding limitation of claims 1, 8, and 15 of the copending application simply recites “executing the Bayesian crop model to predict a crop type, a planting date, and a harvest date for the corresponding field.” (b) Dependent claims 6, 7, 13, 14, 19, and 20 of the instant application refer to “the crop type, the planting date, the emergence date, and the harvest date” while dependent claims 6, 7, 13, 14, 19, and 20 of the copending application simply refer to “the crop type, the planting date, and the harvest date.” Elkin et al. (US 2023/0316116) addresses the gaps between the claim sets in the two applications in its disclosure of the following: [0109] As an option, said one or more crop models comprise at least one base model conditioned on at least two crop stages in a previous agricultural season. As an option, said at least one base model is trained using annotated historical common land unit data, in order to predict said at least two crop states in an agricultural season following the previous agricultural season. As an option, said at least two crop states in the agricultural season are calculated at least in part from said seasonal image data. As an option, said at least one base model is configured to generate the forecast of said at least one crop state based on said seasonal image data. As an option, each crop state is a crop type, a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest date, or a damage to crop. As an option, the seasonal image data is processed with respect to each pixel of an image corresponding to a crop planted in said at least one agricultural field. [0110] As an option, further comprising: configuring the Bayesian framework to model a crop state in a previous agricultural season using seasonal image data of the previous agricultural season; and recalibrating said one or more probabilities based on the configured Bayesian framework, wherein said one or more probabilities are adapted to outputs of said one or more crop models. As an option, the Bayesian framework is configured to: classify, based on a crop type, at least one crop from at least one subset of the seasonal image data; determine said one or more probabilities for each classified crop; and update the Bayesian framework based on the classification in relation to said one or more probabilities. As an option, said one or more crop models comprises crop planting date prediction model, crop yield prediction model, crop acreage model, cover crop model, crop emergence date model, crop harvest model, and crop damage model. As an option, each crop model is configured to generate, based on said one or more probabilities, a crop state prediction associated with said at least one agricultural field in relation to the seasonal image data from at least one agricultural season. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify claims 1-20 of copending Application No. 18/649,935 to incorporate the operation of “executing the Bayesian crop model to predict a crop type, a planting date, and an emergence date, and a harvest date for the corresponding field” (as recited in independent claims 1, 8, and 15 of the instant application, with further reference to “the crop type, the planting date, the emergence date, and the harvest date” being made in dependent claims 6, 7, 13, 14, 19, and 20 of the instant application) in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (c) Independent claims 1, 8, and 15 of the instant application recite the following limitations that are not recited in the claims of the related application: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables; constructing hierarchical prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages; and performing probabilistic inference over the phenological parameter sets within the hierarchical prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application to perform the step of: fitting parametric phenological functions comprising crop vegetation index double-sigmoid functions to the composite estimated growth curves to generate corresponding phenological parameter sets, wherein the phenological parameter sets correspond to biologically interpretable growth-stage transition variables “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and because “[c]ompared with single-date remote sensing images, time-series remote sensing contains more information about a crop’s biophysical features derived from multi-temporal images. In particular, time series can reveal spectral changes reflecting changes in phenology (Bai et al. 2020). Time series have been widely used in crop classification, and the accuracy of the classifications based on time series is better than that of classifications based on mono-temporal remote sensing…” (Zhang: p. 627) Elkin discloses: constructing prior distributions of the Bayesian crop model using the phenological parameter sets as constrained probabilistic variables governing inference over crop growth stages (¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 65 – “The update may be constrained by the weighted confidence predictions of each crop model.”); and performing probabilistic inference over the phenological parameter sets within the prior distributions to generate estimated second associated posterior distribution parameters, and using the estimated second associated posterior distribution parameters to generate the crop type, the planting date, the emergence date, and the harvest date (Elkin: ¶ 36 – “A crop state may be a type of crop type, time passed after a crop planting date, a crop yield, a crop acreage, a crop emergence date, a crop harvest, or damage to the crop.”; ¶ 37 – crop type; ¶ 38 – “crop planting date; ¶ 40 – crop emergence date; ¶ 41 – crop harvest date; ¶¶ 109-110; ¶¶ 82-89 – Prior probably distributions may be inferred. Models may be updated, e.g. for a new season. Predicted probabilities are determined.; ¶ 54 – “Each crop model may further comprise a base model conditioned on at least two crop states in a previous agricultural season. The base model is representative of a prior probability distribution used for predicting the state of the crop in the subsequent agricultural season or in the next iteration of recalibrating the same or additional crop models.”). Elkin does not explicitly disclose that the prior distributions of the Bayesian crop model are hierarchical. Jiang states, “The objective of this analysis was to apply a spatial Bayesian hierarchical model to examine the effects of soil, topographic and climate variables on corn yield.” (Jiang: p. 111: abstract) Relationships based on prior distributions and posterior distributions are evaluated (Jiang: p. 113). The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims of the related application such that the prior distributions of the Bayesian crop model are hierarchical in order to reap the benefits of a Bayesian hierarchical approach to agricultural management, as explained in the following paragraph from pages 123-124 of Jiang: PNG media_image1.png 182 482 media_image1.png Greyscale PNG media_image2.png 128 478 media_image2.png Greyscale Such modifications would have been further beneficial in order to facilitate “delivering crop-related forecasting based on one or more crop states in a more accurate and reliable manner while overcoming the disadvantages in the existing solutions such as missed or ignored attributes during data processing and the at least partial disregarded of seasonality in data when deploying sequential machine learning methods.” (Elkin: ¶ 47). (d) Regarding claims 2, 9, and 16, the corresponding claims in the related application do not fully recite wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets. Elkin uses a Bayesian framework to train its crop models for one or more fields. Zhang acknowledges that certain images have missing data (such as due to cloud cover) and such gaps need to be corrected and may be corrected using information from adjacent values in the time series. Zhang also uses multi-spectral images. Zhang does not explicitly go through a cleansing process of removing and retaining images and then replacing missing data with time-adjacent image data; however, Allan makes up for these deficiencies by disclosing a satellite imaging system and method that monitor changes in vegetation (such as crop growth) over time, including over months or years (Allan: ¶¶ 4, 50-51, 65). Occluded parts of an image may be replaced by non-occluded images (Allan: ¶ 14) and the line between an image being “occluded” vs. “non-occluded” may be the threshold mark below which an image is not sufficient and needs to be replaced. Non-occluded images are understood to be okay for use and are retained. A composite image may be formed to compensate for gaps left by cloud obscuration to create a cloud-free image (Allan: ¶¶ 47-48) and the next most recent image is iteratively evaluated until a non-occluded image is identified to fill in the missing image data (Allan: ¶¶ 13, 54). Allan provides a possible approach for Zhang’s image analysis to correct for missing image data due to cloud occlusion. The purpose of filling in gaps in a series of time-based data is to provide temporal continuity. The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein replacement of the second missing data employs interpolated data generated from time-processing of the third data from the other time-adjacent images, wherein the interpolated data preserves temporal continuity of the composite estimated growth curves used to derive the phenological parameter sets in order to prevent cloud occlusion in imagery while using the most up to date image information possible (as suggested in ¶ 12 of Allan), with the crop-specified benefit of facilitating the encouragement or discouragement of growth of certain crops (as suggested in ¶ 50 of Allan). (e) Regarding claims 3, 10, and 17, the corresponding claims in the related application do not fully recite wherein the Bayesian crop model approximates a posterior distribution over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Elkin discloses wherein the Bayesian crop model approximates a posterior distribution of parameters (Elkin: ¶ 46 – “The Bayesian framework derives from the seasonal data (or historical data) prior probability distribution or referring herein as prior or prior probability. The Bayesian framework uses the prior probability distribution and a likelihood function, or joint probability of the seasonal image as a function of the parameters of a crop model, to produce a posterior probability distribution and provide thereafter said one or more probabilities of a crop state. For each crop state or herein described crop model, the Bayesian framework may separately designate, for each crop model, a density of a random variable whose probability distribution is continuous with respect to model input.”). Elkin does not explicitly disclose that the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution. Zhang states, “Due to differences in environmental factors, the phenology of the same crop is different every year, causing divergent performances of the classifier built by spectral or time-series features Here, we proposed a random forest classifier (RFC) based on an asymmetric double S curve model fitted by accumulated temperature (AT) and Vegetation Index (VI), which can be applied in different years without ground samples. We built AT and VI time series from Moderate Resolution Imaging Spectroradiometer 8-day composites of land surface temperatures and Sentinel-2 and Landsat-8, respectively. The RFC was trained by characteristics from the asymmetric double S curve. We prepared RFC by ground samples of 2018 and 2019 and then mapped crops of the same region in 2017.” (Zhang: p. 626, abstract) Zhang further explains that “[w]e used the asymmetric double-sigmoid function proposed by Zhong et al. (2011), because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics.” (Zhang: p. 635) Zhang does not explicitly disclose “using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution.” In an agronomic environment, Richt describes the benefit of using Hamiltonian Markov chain Monte Carlo (MCMC) as follows: “[0197] Values for agronomic inputs for a farmable region can be determined using different metaheuristic techniques, such as a Markov chain Monte Carlo (MCMC) and approximate Bayesian computations or Simulated Annealing. Other metaheuristics can include genetic algorithms, differential evolution, particle swarm optimization, ant colony algorithms, tabu search, stochastic gradient ascent/descent, simultaneous perturbation stochastic approximation (SPSA), Differential Evolution Adaptive Metropolis (DREAM), and Hamiltonian MCMC. These methods enable the solution of optimization problems in large dimensional spaces.” The Examiner submits that it would have been obvious to one of ordinary skill in the art before the effective filing date of Applicant’s invention to modify the claims in the related application wherein the posterior distribution of parameters is over the phenological parameter sets corresponding to parameters of the double-sigmoid function given a set of observations corresponding to the second remote sense images using a Hamiltonian Monte Carlo algorithm to generate samples of the posterior distribution “because compared with the double logistic model or the straightforward definition of the linear harmonic model, the asymmetric double-sigmoid function would reveal spectral characteristics of vegetation during the nutrition-accumulation stage and provide a good balance between model complexity and the ability to reveal crop spectral characteristics” (Zhang: p. 635) and in order to “enable the solution of optimization problems in large dimensional spaces” (Richt: ¶ 197). (f) The related application recites some limitations not recited in the claims of the instant application. Elimination of an element or its functions is deemed to be obvious in light of prior art teachings of at least the recited element or its functions (see In re Karlson, 136 USPQ 184, 186; 311 F2d 581 (CCPA 1963)). This is a provisional nonstatutory double patenting rejection because the patentably indistinct claims have not in fact been patented. Conclusion The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. Ebrahimi Afrouzi et al. (US 2022/0066456) – Performs Bayesian inference with prior and posterior information and assigns probabilities to model parameters to generate Bayesian hierarchical modeling (¶ 1175). Also discusses the use of S curves (¶ 822). Sun et al. (US 2019/0080246) – Generates a hierarchical Bayesian model with sub-models and prior and posterior distributions (¶¶ 10, 43). Zhang et al. (CN 113933896 A) – Discusses Bayesian models with posterior probability distribution and adaptive prior distribution (abstract). Any inquiry concerning this communication or earlier communications from the examiner should be directed to SUSANNA M DIAZ whose telephone number is (571)272-6733. The examiner can normally be reached M-F, 8 am-4:30 pm. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Brian Epstein can be reached at (571) 270-5389. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /SUSANNA M. DIAZ/ Primary Examiner Art Unit 3625A
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Prosecution Timeline

Apr 29, 2024
Application Filed
Jul 28, 2025
Non-Final Rejection mailed — §103, §112, §DOUBLEPATENT
Oct 28, 2025
Response Filed
Feb 11, 2026
Final Rejection mailed — §103, §112, §DOUBLEPATENT
Mar 24, 2026
Request for Continued Examination
Apr 01, 2026
Response after Non-Final Action
Apr 07, 2026
Non-Final Rejection mailed — §103, §112, §DOUBLEPATENT (current)

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