Gibbs sampling, adaptive rejection sampling and robustness to prior specification for a mixed linear model

A - Papers appearing in refereed journals

Theobald, C. M., Firat, M. Z. and Thompson, R. 1997. Gibbs sampling, adaptive rejection sampling and robustness to prior specification for a mixed linear model. Genetics Selection Evolution. 29 (1), pp. 57-72.

AuthorsTheobald, C. M., Firat, M. Z. and Thompson, R.
Abstract

Markov chain Monte-Carlo methods are increasingly being applied to make inferences about the marginal posterior distributions of parameters in quantitative genetic
models. This paper considers the application of one such method, Gibbs sampling, to Bayesian inferences about parameters in a normal mixed linear model when a restriction
is imposed on the relative values of the variance components. Two prior distributions are proposed which incorporate this restriction. For one of them, the adaptive rejection
sampling technique is used to sample from the conditional posterior distribution of a variance ratio. Simulated data from a balanced sire model are used to compare
different implementations of the Gibbs sampler and also inferences based on the two prior distributions. Marginal posterior distributions of the parameters are illustrated. Numerical results suggest that it is not necessary to discard any iterates, and that similar inferences are made using the two prior specifications.

Keywordsadaptive rejection sampling; Bayesian inference; Gibbs sampling; mixed linear model ; sire model
Year of Publication1997
JournalGenetics Selection Evolution
Journal citation29 (1), pp. 57-72
Digital Object Identifier (DOI)doi:10.1186/1297-9686-29-1-57
PubMed Central IDPMC2708200
Open accessPublished as ‘gold’ (paid) open access
Funder project or code207
445
Project: 141433
Publisher's version
Output statusPublished
Publication dates
Online15 Apr 1997
Publication process dates
Accepted13 Jan 1997
Copyright licenseCC BY
PublisherBiomed Central Ltd
ISSN0999-193X

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