Wiener-chaos analysis on Bayesian models with applications in agriculture and climatology

Understanding the challenges to increasing maize productivity in sub-Saharan Africa has important implications for policies to reduce national and global food insecurity. There is insufficient research on the key agronomic and environmental factors that influence maize yield in a smallholder-farm environment. We implement a Bayesian analysis with longitudinal household survey data covering 1,197 plots among 320 farms in central Malawi. The results reveal a high positive association between a leaf chlorophyll indicator and yield, with significance levels exceeding 95% Bayesian credibility at all sites, and the posterior mean of the regression coefficient ranging from 28% to 42% on a relative scale. A parasitic weed, Striga asiatica, is the variable that negatively associated with yield of high intensity. The impact of rainfall varies by site and season, either directly or indirectly. We conclude that the determinants preventing striga infestation and enhancing nitrogen fertility will lead to higher maize yield in Malawi. To improve plant nitrogen status, fertilizer is effective at higher-productivity sites, whereas soil carbon and organic inputs are important at marginal sites. Uniquely, the Bayesian approach allows differentiation of response by site for a modest-sample-size study. Considering the biophysical constraints, our findings highlight area-specific recommendations as well as management strategies for crop yield.Quantifying the sensitivity of climate forcing factors such as greenhouse gas concentration and solar irradiation, is critical in comprehending the evolution of the Earth's climate. There exists a variety of statistical methods to reconstruct temperature in the past, but the same is not true for projecting future temperatures. We produce a multi-level stochastic model to systematically reconstruct and project the northern-hemisphere average temperature anomalies, for the past millennium (1000-1999) and the next century (2019-2100), by coordinating with climatic forcings and natural proxies from diverse data sources. Additive noises are applied to the model to capture the unaccounted variability. Model parameters are estimated using Bayesian-inference techniques, resulting in complete distributional information. Reconstructions with memory features (no, short, long) are evaluated through selected validation metrics, and the results constitute evidence in favor of using a moderate-memory length. For the purpose of temperature projections, we incorporate realistic climate forcing uncertainties to Year 2100. Similarly, we include an uncertainty component on top of using representative carbon pathway scenarios for global greenhouse gases. Our projections' posterior means show a great level of agreement with the 95% confidence interval provided by the Coupled Model Intercomparison Project, while featuring differences in most cases.The models described above are both implemented via Gibbs sampler with 10,000 iterations. In order to avoid its potential computational heft, we combine the use of maximum likelihood estimators for regression elements with properties of Wiener chaos, to approximate the predictive samples with specific chaos distributions that do not require sampling via numerics. Some of the approximations' statistics, such as error variances are also explicitly provided. The precision are relatively high (nearly 0.1% and 0.5%) depending on dimension circumstances. This allows practitioners to estimate approximation accuracy and convergence rates in practice, with no resort to heavy computational demands.