On the ergodicity properties of some adaptive MCMC algorithms

Details On the ergodicity properties of some adaptive MCMC algorithms On the ergodicity properties of some adaptive MCMC algorithms

2006-10-10

arxiv.org/abs/math/0610317v1

Annals of Applied Probability 2006, Vol. 16, No. 3, 1462-1505

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000286 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000286

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the independent Metropolis--Hastings algorithm and the random walk Metropolis algorithm with symmetric increments. Finally, we propose an application of these results to the case where the proposal distribution of the Metropolis--Hastings update is a mixture of distributions from a curved exponential family.

Affiliated with

Also associated with

No associations

Rating

On the ergodicity properties of some adaptive MCMC algorithms 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 On the ergodicity properties of some adaptive MCMC algorithms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the ergodicity properties of some adaptive MCMC algorithms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438134