A Bayesian approach for estimating and checking block designs in agricultural experiments

Abstract

Spatial blocking is a common technique used in designed agricultural experiments. Spatial blocking, however, requires two important assumptions: 1) the spatial blocks can be clearly delineated within a field by an expert; and 2) the area within each block is homogeneous. Statistical analyses of blocked agricultural experiments often show spatially correlated residuals, suggesting one of the assumptions mentioned above was not met. We propose a model for estimating block membership with data, as an alternative method to account for spatial effects, while preserving the traditional designed experiment framework. We embed a classification and regression tree within a Bayesian statistical model, to estimate block membership. We illustrate possible applications of this approach with some of the most typical scenarios we have encountered in our applied experience in agricultural research with four synthetic data sets and two field data sets. Our hybrid Bayesian-Machine Learning approach can serve one of two purposes: validating the originally designed block layout, or estimating the spatial block layout. Thus, this model provides researchers with a flexible tool for analyzing designed agricultural experiments.