Convergence Rates for Hierarchical Gibbs Samplers
Probability
2014-12-08 v2
Abstract
We establish some results for the rate of convergence in total variation of a Gibbs sampler to its equilibrium distribution. This sampler is motivated by a hierarchical Bayesian inference construction for a gamma random variable. Our results apply to a wide range of parameter values in the case that the hierarchical depth is 3 or 4, and are more restrictive for depth greater than 4. Our method involves showing a relationship between the total variation of two ordered copies of our chain and the maximum of the ratios of their respective co-ordinates. We construct auxiliary stochastic processes to show that this ratio does converge to 1 at a geometric rate.
Cite
@article{arxiv.1402.4733,
title = {Convergence Rates for Hierarchical Gibbs Samplers},
author = {Oliver Jovanovski and Neal Madras},
journal= {arXiv preprint arXiv:1402.4733},
year = {2014}
}