Gibbs/Metropolis algorithms on a convex polytope
Spectral Theory
2011-04-06 v1 Probability
Abstract
This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyl-type inequalities. The top eigenvalues of the Markov chain are closely related to the Neuman eigenvalues of the polytope for a novel Laplacian.
Cite
@article{arxiv.1104.0749,
title = {Gibbs/Metropolis algorithms on a convex polytope},
author = {Persi Diaconis and Gilles Lebeau and Laurent Michel},
journal= {arXiv preprint arXiv:1104.0749},
year = {2011}
}
Comments
21 pages, 1 figure