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Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions

Karawatzki, Roman and Leydold, Josef and Pötzelberger, Klaus (2005) Automatic Markov Chain Monte Carlo Procedures for Sampling from Multivariate Distributions. Research Report Series / Department of Statistics and Mathematics, 27. Department of Statistics and Mathematics, 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. An implementation of these algorithms in C is available from the <a href="http://statmath.wu-wien.ac.at/software/hitro/">authors</a>. (author's abstract)

Item Type: Paper
Keywords: hit-and-run sampling / Markov chain Monte Carlo / multivariate random variate generation / ratio-of-uniforms method / log-concave distributions
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 23 Dec 2005 14:16
Last Modified: 15 May 2015 00:07
URI: http://epub.wu.ac.at/id/eprint/1400

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