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Abstract With climate change threatening agricultural productivity and global food demand increasing, it is important to better understand which farm management practices will maximize crop yields in various climatic conditions. To assess the effectiveness of agricultural practices, researchers often turn to randomized field experiments, which are reliable for identifying causal effects but are often limited in scope and therefore lack external validity. Recently, researchers have also leveraged large observational datasets from satellites and other sources, which can lead to conclusions biased by confounding variables or systematic measurement errors. Because experimental and observational datasets have complementary strengths, in this paper we propose a method that uses a combination of experimental and observational data in the same analysis. As a case study, we focus on the causal effect of crop rotation on corn (maize) and soybean yields in the Midwestern United States. We find that, in terms of root mean squared error, our hybrid method performs 13% better than using experimental data alone and 26% better than using the observational data alone in the task of predicting the effect of rotation on corn yield at held-out experimental sites. Further, the causal estimates based on our method suggest that benefits of crop rotations on corn yield are lower in years and locations with high temperatures whereas the benefits of crop rotations on soybean yield are higher in years and locations with high temperatures. In particular, we estimated that the benefit of rotation on corn yields (and soybean yields) was 0.85 t ha⁻¹(0.24 t ha⁻¹) on average for the top quintile of temperatures, 1.03 t ha⁻¹(0.21 t ha⁻¹) on average for the whole dataset, and 1.19 t ha⁻¹(0.16 t ha⁻¹) on average for the bottom quintile of temperatures. This association between temperatures and rotation benefits is consistent with the hypothesis that the benefit of the corn-soybean rotation on soybean yield is largely driven by pest pressure reductions while the benefit of the corn-soybean rotation on corn yields is largely driven by nitrogen availability. 

Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are o(1/n) as n → ∞, and randomized versions can attain root mean squared errors that are o(1/n), changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points can be very detrimental to QMC performance. These include thinning, burn-in, and taking sample sizes such as powers of 10, when the QMC points were designed for different sample sizes. This article looks at the effects of a common practice in which one skips the first point of a Sobol’ sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to √n where n is the number of function evaluations used. 

Conditional density estimation is a fundamental problem in statistics, with scientific and practical applications in biology, economics, finance and environmental studies, to name a few. In this paper, we propose a conditional density estimator based on gradient boosting and Lindsey’s method (LinCDE). LinCDE admits flexible modeling of the density family and can capture distributional characteristics like modality and shape. In particular, when suitably parametrized, LinCDE will produce smooth and non-negative density estimates. Furthermore, like boosted regression trees, LinCDE does automatic feature selection. We demonstrate LinCDE’s efficacy through extensive simulations and three real data examples.