Hierarchical Bayesian Modeling In Agricultural Research: Reconciling Irreproducibility With Heterogeneity and Scope Of Inference.

Agriculturalists, like many other experimental scientists, typically conduct research with somewhat limited scope of inference (i.e., work conducted within one or a few years within one or a few locations). This potentially raises the specter of reproducibility (or lack thereof) of inferences between similar research projects conducted at multiple stations, often due to the lack of appreciation of scope of inference that could only reasonably be addressed by hierarchical modeling of effects across environments.  Hierarchical Bayesian analysis more or less represents extensions of mixed effects modeling that is already commonplace in the analysis of agricultural research data.  That is, efficient experiments are typically based on design structures that are defined by random effects, such as plots, subplots, years, etc., including those that distinguish, say, observational from experimental units.  Hierarchical Bayesian analyses have been readily utilized by agricultural quantitative geneticists because of a “large p, small n” problem that typically nullifies the use of commonly used statistical procedures based on large sample approximations.  At first glance, this problem may not seem to be emblematic of other types of agricultural/natural resource research.   However, it can be particularly acute in generalized linear mixed model (GLMM) analyses of rather typical agricultural experiments, depending upon the distribution of the data and the complexity of the experimental design.  Hierarchical Bayesian model constructions also allow investigators to efficiently explore other phenomena that could not be otherwise addressed using more conventional GLMM approaches.   Substantially enhanced computing resources and algorithmic developments allow Bayesian analyses to be far more tractable than they were just a couple of decades ago.