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Comparison of hit-and-run, slice sampler and random walk Metropolis

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  16 January 2019

Daniel Rudolf  and
Mario Ullrich
Daniel Rudolf*
Affiliation:
Universität Göttingen
Mario Ullrich*
Affiliation:
Universität Linz
*
* Postal address: Felix-Bernstein-Institute for Mathematical Statistics in the Biosciences, Universität Göttingen, Goldschmidstraße 7, 37077 Göttingen, Germany. Email address: daniel.rudolf@uni-goettingen.de
** Postal address: Universität Linz, Altenberger Straße 69, 4040 Linz, Austria. Email address: mario.ullrich@jku.at
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Abstract

Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler, and random walk Metropolis algorithm are popular tools to simulate such Markov chains. We develop a general approach to compare the efficiency of these sampling procedures by the use of a partial ordering of their Markov operators, the covariance ordering. In particular, we show that the hit-and-run and the simple slice sampler are more efficient than a hybrid slice sampler based on hit-and-run, which, itself, is more efficient than a (lazy) random walk Metropolis algorithm.

Keywords

Hit-and-runslice samplerrandom walk Metropoliscovariance ordering

MSC classification

Primary: 60J22: Computational methods in Markov chains
Secondary: 65C05: Monte Carlo methods 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1186 - 1202
Copyright
Copyright © Applied Probability Trust 2018 

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