Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities

Peter Neal () and Gareth Roberts ()
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Peter Neal: University of Manchester
Gareth Roberts: Lancaster University

Methodology and Computing in Applied Probability, 2008, vol. 10, issue 2, 277-297

Abstract: 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.

Keywords: Random walk Metropolis algorithm; Markov chain Monte Carlo; Optimal scaling; Spherical distributions; Primary 60F05; Secondary 65C05 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11009-007-9046-2

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