Precise estimation and uncertainty quantification for average crop yields are critical for agricultural monitoring and decision making. Existing data collection methods, such as crop cuts in randomly sampled fields at harvest time, are relatively time-consuming. Thus, we propose an approach based on prediction-powered inference (PPI) to supplement these crop cuts with less time-consuming field photos. After training a computer vision model to predict the ground truth crop cut yields from the photos, we learn a ``control function" that recalibrates these predictions with the spatial coordinates of each field. This enables fields with photos but not crop cuts to be leveraged to improve the precision of zone-wide average yield estimates. Our control function is learned by training on a dataset of nearly 20,000 real crop cuts and photos of rice and maize fields in sub-Saharan Africa. To improve precision, we pool training observations across different zones within the same first-level subdivision of each country. Our final PPI-based point estimates of the average yield are provably asymptotically unbiased and cannot increase the asymptotic variance beyond that of the natural baseline estimator -- the sample average of the crop cuts -- as the number of fields grows. We also propose a novel bias-corrected and accelerated (BCa) bootstrap to construct accompanying confidence intervals. Even in zones with as few as 20 fields, the point estimates show significant empirical improvement over the baseline, increasing the effective sample size by as much as 73% for rice and by 12-23% for maize. The confidence intervals are accordingly shorter at minimal cost to empirical finite-sample coverage. This demonstrates the potential for relatively low-cost images to make area-based crop insurance more affordable and thus spur investment into sustainable agricultural practices.

翻译：对平均作物产量的精确估算与不确定性量化是农业监测与决策制定的关键。现有数据收集方法（例如在收获期对随机抽样田地进行作物切割）相对耗时。因此，我们提出一种基于预测驱动推断（PPI）的方法，通过耗时较少的田间照片来补充这些作物切割数据。在训练计算机视觉模型从照片预测真实作物切割产量后，我们学习一种“控制函数”，该函数利用每个田地的空间坐标对这些预测进行重新校准。这使得拥有照片但未进行作物切割的田地能够被用于提高区域范围平均产量估算的精度。我们的控制函数通过在近20,000个真实作物切割数据及撒哈拉以南非洲地区水稻和玉米田照片组成的数据集上进行训练而习得。为提高精度，我们在每个国家同一一级行政区划内的不同区域间汇集训练观测数据。我们最终基于PPI的平均产量点估计在理论上具有渐近无偏性，且随着田地数量增加，其渐近方差不会超过自然基线估计量（即作物切割的样本均值）的方差。我们还提出一种新颖的偏差校正加速（BCa）自助法来构建相应的置信区间。即使在仅有20块田地的区域，点估计也显示出相较于基线的显著经验改进，将水稻的有效样本量提升高达73%，玉米提升12-23%。相应地，置信区间在经验有限样本覆盖率损失极小的前提下更短。这证明了相对低成本的图像在使基于区域的作物保险更可负担、从而激励可持续农业实践投资方面的潜力。