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In plant breeding the presence of a genotype by environment (GxE) interactionhas a strong impact on cultivation decision making and the introduction of newcrop cultivars. The combination of linear and bilinear terms has been shown tobe very useful in modelling this type of data. A widely-used approach toidentify GxE is the Additive Main Effects and Multiplicative InteractionEffects (AMMI) model. However, as data frequently can be high-dimensional,Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible.In this article, we consider a variational inference approach for such a model.We derive variational approximations for estimating the parameters and wecompare the approximations to MCMC using both simulated and real data. The newinferential framework we propose is on average two times faster whilstmaintaining the same predictive performance as MCMC.

Variational Inference for Additive Main and Multiplicative Interaction Effects Models