The paper describes Bayesian analysis for agricultural field experiments, a
topic that has received very little previous attention, despite a vast fre
quentist literature. Adoption of the Bayesian paradigm simplifies the inter
pretation of the results, especially in ranking and selection. Also, comple
x formulations can be analysed with comparative ease. by using Markov chain
Monte Carlo methods. A key ingredient in the approach is the need for spat
ial representations of the unobserved fertility patterns. This is discussed
in detail. Problems caused by outliers and by jumps in fertility are tackl
ed via hierarchical-t formulations that may find use in other contexts. The
paper includes three analyses of variety trials for yield and one example
involving binary data; none is entirely straightforward. Some numerical com
parisons with frequentist analyses are made.