Shrinkage effect in the Bayesian analysis of the GGE model using maximum entropy prior
In this work, the maximum entropy principle was used to assign a priori information to the variance components of the singular values in the genotype main effects model plus genotype×environment interaction (GGE). The method was exemplified from simulated data. The results showed that the GGE model with maximum entropy priori (BGGEE) produces a shrinkage effect on the estimates of singular values, when compared with the frequentist GGE analysis or with the Bayesian GGE version that uses non-informative priors (referred to by BGGE). The BGGEE showed greater parsimony, estimating the singular values with greater contribution to the interaction effect and shrinking the estimates of singular values associated with larger dimensions to zero. Thus, BGGEE captured more pattern and discarded more noise than the typical Bayesian version. When using maximum entropy priori, it was found that the complete model and the one with only two bilinear terms are almost indistinguishable. This signals that model selection in the BGGEE fit would not be a necessary step. The method also avoids sampling problems observed when Jeffreys prior are used, resulting in proper and unimodal posterior marginal distributions.
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