Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors

Details Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors

2011-11-14

arxiv.org/abs/1111.3210v1

Mathematics

Statistics Theory

Scientific paper

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple Gibbs sampler that can be employed to explore the posterior density. A popular default among the conditionally conjugate priors is an improper prior that takes a product form with a flat prior on the regression parameter, and so-called power priors on each of the variance components. In this paper, a convergence rate analysis of the corresponding Gibbs sampler is undertaken. The main result is a simple, easily-checked sufficient condition for geometric ergodicity of the Gibbs Markov chain. This result is close to the best possible result in the sense that the sufficient condition is only slightly stronger than what is required to ensure posterior propriety. The theory developed in this paper is extremely important from a practical standpoint because it guarantees the existence of central limit theorems that allow for the computation of valid asymptotic standard errors for the estimates computed using the Gibbs sampler.

Affiliated with

Also associated with

No associations

Rating

Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-218277