Optimal Scaling for Random walk Metropolis on spherically constrained target densities

Neal, Peter and Roberts, Gareth (2006) Optimal Scaling for Random walk Metropolis on spherically constrained target densities. [MIMS Preprint]

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Abstract

We consider the problem of optimal scaling of the proposal variance for multidimensional Random walk Metropolis (RWM) 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 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.

Item Type: MIMS Preprint
Additional Information: Submitted to Methodology and Computing in Applied Probability
Uncontrolled Keywords: Random walk Metropolis algorithm, Markov chain Monte Carlo, optimal scaling, spherical distributions.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User: Dr Peter Neal
Date Deposited: 20 Dec 2006
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/676

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