Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition

Details Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition

2009-03-04

arxiv.org/abs/0903.0664v3

Statistics

Computation

Scientific paper

It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional distribution associated with the target this is just a Gibbs sampler. Often at least one of the Gibbs updates is replaced with a Metropolis-Hastings step yielding a Metropolis-Hastings-within-Gibbs algorithm. Strategies for combining component-wise updates include composition, random sequence and random scans. While these strategies can ease MCMC implementation and produce superior empirical performance compared to full-dimensional updates, the theoretical convergence properties of the associated Markov chains have received limited attention. We present conditions under which some component-wise Markov chains converge to the stationary distribution at a geometric rate. We pay particular attention to the connections between the convergence rates of the various component-wise strategies. This is important since it ensures the existence of tools that an MCMC practitioner can use to be as confident in the simulation results as if they were based on independent and identically distributed samples. We illustrate our results in two examples including a hierarchical linear mixed model and one involving maximum likelihood estimation for mixed models.

Affiliated with

Also associated with

No associations

Rating

Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition 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 Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Component-wise Markov chain Monte Carlo: Uniform and Geometric Ergodicity Under Mixing and Composition will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-368421