Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

• Published in: Heredity Vol. 109; no. 4; pp. 235 - 245
• Main Authors: Mathew, B, Bauer, A M, Koistinen, P, Reetz, T C, Léon, J, Sillanpää, M J
• Format: Journal Article
• Language: English
• Published: England Springer Nature B.V 01-10-2012; Nature Publishing Group
• Subjects: Algorithms; Barley; Bayes Theorem; Bayesian analysis; Breeding - statistics & numerical data; Computer Simulation; Data processing; Dominance; Genetics; Hordeum vulgare; Hybrids; Learning; Likelihood Functions; Linear Models; Markov Chains; Mathematical models; Models, Genetic; Monte Carlo Method; Original; Parameter estimation; Plant breeding; Quantitative Trait, Heritable; Samplers; Sampling
• ISSN: 0018-067X; 1365-2540
• DOI: 10.1038/hdy.2012.35

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.