Gibbs/Metropolis algorithms on a convex polytope

Details Gibbs/Metropolis algorithms on a convex polytope Gibbs/Metropolis algorithms on a convex polytope

2011-04-05

arxiv.org/abs/1104.0749v1

Mathematics

Spectral Theory

21 pages, 1 figure

Scientific paper

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.

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