Hit-and-run for numerical integration

Abstract

We study the numerical computation of an expectation of a bounded function with respect to a measure given by a non-normalized density on a convex body. We assume that the density is log-concave, satisfies a variability condition and is not too narrow. We consider general convex bodies or even the whole ${\mathbb{R}}^d$ and show that the integration problem satisfies a refined form of tractability. The main tools are the hit-and-run algorithm and an error bound of a multi run Markov chain Monte Carlo method.

References in corpus (1)

• Rapid mixing of Swendsen-Wang and single-bond dynamics in two dimensions

Cited by in corpus (4)

• Convergence of hybrid slice sampling via spectral gap
• Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
• Computation of expectations by Markov chain Monte Carlo methods
• Comparison of hit-and-run, slice sampling and random walk Metropolis