A fast and efficient Gibbs sampler for BayesB in whole-genome analyses.

Dorian J Garrick,Long Qu,Rohan L Fernando,Hao Cheng

doi:10.1186/s12711-015-0157-x

Dorian J Garrick, Long Qu + Show 2 more

Open Access

https://doi.org/10.1186/s12711-015-0157-x

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Abstract

Background In whole-genome analyses, the number p of marker covariates is often much larger than the number n of observations. Bayesian multiple regression models are widely used in genomic selection to address this problem of pgg n. The primary difference between these models is the prior assumed for the effects of the covariates. Usually in the BayesB method, a Metropolis–Hastings (MH) algorithm is used to jointly sample the marker effect and the locus-specific variance, which may make BayesB computationally intensive. In this paper, we show how the Gibbs sampler without the MH algorithm can be used for the BayesB method.ResultsWe consider three different versions of the Gibbs sampler to sample the marker effect and locus-specific variance for each locus. Among the Gibbs samplers that were considered, the most efficient sampler is about 2.1 times as efficient as the MH algorithm proposed by Meuwissen et al. and 1.7 times as efficient as that proposed by Habier et al.ConclusionsThe three Gibbs samplers presented here were twice as efficient as Metropolis–Hastings samplers and gave virtually the same results.

Highlights

In whole-genome analyses, the number p of marker covariates is often much larger than the number n of observations
The marginal distribution of y, the denominator of (7), does not depend on the pseudo prior, which is the distribution of βj when δj = 0. As both the numerator and denominator of (1) are free of the pseudo prior, it follows that the posterior mean of αj does not depend on the pseudo prior for βj. Given this pseudo prior, the full conditional for δj is identical to the marginal full conditional distribution of δj, Pr δj|y, μ, β−j, δ−j, ξ, σe2, which is used in the joint Gibbs sampler
The number of effective samples per second of computing time was obtained for BayesB using MH, efficient MH or the three different Gibbs samplers

Summary

Introduction

In whole-genome analyses, the number p of marker covariates is often much larger than the number n of observations. The primary difference between these models is the prior assumed for the effects of the covariates. In most Bayesian analyses of whole-genome data, inferences are based on Markov chains constructed to have a stationary distribution equal to the posterior distribution of the unknown parameters of interest [2]. This is often done by employing a Gibbs sampler where samples are drawn from the full-conditional distributions of the parameters [3]

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