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Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities

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  • Peter Neal

    (University of Manchester)

  • Gareth Roberts

    (Lancaster University
    University of Warwick)

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.

Suggested Citation

  • Peter Neal & Gareth Roberts, 2008. "Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 277-297, June.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:2:d:10.1007_s11009-007-9046-2
    DOI: 10.1007/s11009-007-9046-2
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    References listed on IDEAS

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    1. Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    2. Breyer, L. A. & Roberts, G. O., 2000. "From metropolis to diffusions: Gibbs states and optimal scaling," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 181-206, December.
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    Cited by:

    1. Abbas, Kamran & Tang, Yincai, 2014. "Objective Bayesian analysis of the Frechet stress–strength model," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 169-175.
    2. Peter Neal & Gareth Roberts, 2011. "Optimal Scaling of Random Walk Metropolis Algorithms with Non-Gaussian Proposals," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 583-601, September.
    3. Yang, Jun & Roberts, Gareth O. & Rosenthal, Jeffrey S., 2020. "Optimal scaling of random-walk metropolis algorithms on general target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6094-6132.
    4. Jeong Eun Lee & Ross McVinish & Kerrie Mengersen, 2011. "Population Monte Carlo Algorithm in High Dimensions," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 369-389, June.
    5. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    6. Min Wang & Xiaoqian Sun & Chanseok Park, 2016. "Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method," Computational Statistics, Springer, vol. 31(1), pages 207-225, March.

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