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Nonconjugate Bayesian Analysis of Variance Component Models
Author(s) -
Wolfinger Russell D.,
Kass Robert E.
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.00768.x
Subject(s) - prior probability , markov chain monte carlo , gibbs sampling , computer science , bayesian probability , variance (accounting) , flexibility (engineering) , independence (probability theory) , component (thermodynamics) , markov chain , conjugate prior , algorithm , mathematical optimization , data mining , mathematics , statistics , artificial intelligence , machine learning , physics , accounting , thermodynamics , business
Summary. We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.