An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

Abstract

Computational efficiency is an increasing concern for whole genome prediction (WGP) based on denser genetic marker panels such that algorithms other than Markov Chain Monte Carlo (MCMC) warrant greater consideration, particularly for hierarchical models that flexibly confer either heavy-tailed (e.g., BayesA) or stochastic search and variable selection (SSVS) instead of Gaussian specifications on marker effect distributions. The expectation maximization (EM) algorithm is one attractive alternative; however, recently proposed hierarchical model implementations of EM have not addressed formal estimation of underlying hyperparameters even though their specifications are known to impact WGP accuracy. Furthermore, EM can be sensitive to starting values. We develop and explore the properties of an empirical Bayes strategy by conditioning EM implementations of BayesA or SSVS WGP models on marginal modal estimation of variance components and other key hyperparameters. These empirical Bayes implementations are compared against their MCMC counterparts for estimation of hyperparameters and WGP accuracy, both within the context of a simulation study and application to a loblolly pine dataset. In all cases, starting values were deemed to be important for EM-based estimates. Starting values based on MCMC posterior means were preferable, whereas those based on setting all marker effects equal to zero generally led to inferior performance. Nevertheless, a recently proposed regularization procedure was useful in alleviating the impact of starting values in the EM implementation of the SSVS model, as was modifying the expectation step in the BayesA model to be based on relative variances rather than on relative precisions.

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“…] can be determined using the REML or marginal maximum likelihood (MML) 222 estimation strategies as described byChen and Tempelman (2015) noting that we choose to fix223 …”

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