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Optimal scaling for random walk metropolis on spherically constrained target densities

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>06/2008
<mark>Journal</mark>Methodology and Computing in Applied Probability
Issue number2
Volume10
Number of pages21
Pages (from-to)277-297
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We consider the problem of optimal scaling of the proposal variance for multidimensional random walk Metropolis algorithms. It is well known, for a wide range of continuous target densities, that the optimal scaling of the proposal variance leads to an average acceptance rate of 0.234. Therefore a natural question is, do similar results hold for target densities which have discontinuities? In the current work, we answer in the affirmative for a class of spherically constrained target densities. Even though the acceptance probability is more complicated than for continuous target densities, the optimal scaling of the proposal variance again leads to an average acceptance rate of 0.234.