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Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions

Karawatzki, Roman and Leydold, Josef (2005) Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions. Preprint Series / Department of Applied Statistics and Data Processing, 52. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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Abstract

Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to "conventional methods", especially when many dimensions are involved. In this article we propose a Hit-and-Run sampler in combination with the Ratio-of-Uniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all log-concave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension. (author's abstract)

Item Type: Paper
Keywords: Simulation: multivariate random variate generation / Markov chain Monte Carlo / hit-and-run sampling / ratio-of-uniforms / log-concave distributions
Classification Codes: MSC 65C05, 65C10, 65D30
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 10 Jul 2006 15:43
Last Modified: 18 Jun 2011 02:46
URI: http://epub.wu.ac.at/id/eprint/294

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