Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

Abstract

Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.

<b>Population parameters and selection of kale genotypes using Bayesian inference in a multi-trait linear model

“…They make this approach notably informative (Mathew et al, 2012) and facilitate hypothesis testing. According to Apiolaza, hauhan, and Walker (2011), asymmetric credibility intervals obtained by posterior distribution make the conclusions more realistic than those based on symmetric confidence intervals of frequentist statistics.…”

Integrated nested Laplace approximation inference and cross-validation to tune variance components in estimation of breeding value

“…For the simulation, we first calculated the additive relationship matrix (A) and the dominance relationship matrix (D) from the available pedigree information, then we simulated the data vector, y, using the model y ¼ a þ d þ e. Here the vectors a, and d were drawn from MVNð0; Ar 2 a Þ and MVNð0; Dr 2 d Þ, respectively. In order to draw samples from these multivariate normal distributions, we used the Cholesky decomposition of the covariance matrices Ar 2 a and Dr 2 d (for details, see Mathew et al 2012) after fixing the additive (r 2 a ) and dominance (r 2 d ) variance components to 1,000 and 500 respectively. In comparison, the error vector (e) was sampled from MVNð0; Ir 2 e Þ (here I is the identity matrix) after setting the error variance component (r 2 e ) to 625.…”

“…Various statistical methods have been developed to this end, but the residual (or restricted/reduced) maximum likelihood (REML; Patterson and Thompson 1971) method and the associated software package ASReml (Butler et al 2007) currently dominate the field. However, much effort is also focused on developing new Bayesian estimation tools, including MCMCglmm (Hadfield 2010) adaptiveMCMC (Mathew et al 2012), and AnimalINLA (Holand et al 2013).…”

Comparison of inference methods of genetic parameters with an application to body weight in broilers

“…Recently, Hallander et al (2010) have developed a Bayesian method in WinBUGS based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions, thus permitting the genetic evaluation of complex pedigree structures. In addition, more complicated covariance structures have been incorporated via Bayesian methods, allowing for the simultaneous estimation of both additive and dominance genetic effects Mathew et al, 2012).…”

“…Subsequently, a generalized linear model (McCullagh and Nelder, 1994) was used for the analysis of the binary variable. In this analysis, the observed binary variable y B is related to an underlying unobservable continuous variable λ, such that the observed binary response (y B ) is the result of the following relationship:…”