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On the geometric ergodicity of hybrid samplers

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

Published online by Cambridge University Press:  14 July 2016

G. Fort ,
E. Moulines ,
G. O. Roberts  and
J. S. Rosenthal
G. Fort*
Affiliation:
LMC-IMAG, Grenoble
E. Moulines*
Affiliation:
ENST, Paris
G. O. Roberts*
Affiliation:
Lancaster University
J. S. Rosenthal*
Affiliation:
University of Toronto
*
∗ Postal address: LMC-IMAG, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France. Email address: [email protected]
∗∗ Postal address: ENST, 46 rue Barrault, 75634 Paris Cedex 13, France.
∗∗∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK.
∗∗∗∗ Postal address: Department of Statistics, University of Toronto, 100 St George Street, Toronto, Ontario, Canada M5S 3G3.
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Abstract

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

Keywords

Markov chain Monte Carlohybrid samplergeometric ergodicity

MSC classification

Primary: 65C05: Monte Carlo methods 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 123 - 146
Copyright
Copyright © Applied Probability Trust 2003 

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