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Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions

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  • Kamatani, Kengo

Abstract

High-dimensional asymptotics of the random walk Metropolis–Hastings algorithm are well understood for a class of light-tailed target distributions. Although this idealistic assumption is instructive, it may not always be appropriate, especially for complicated target distributions. We here study heavy-tailed target distributions for the random walk Metropolis algorithms. When the number of dimensions is d, the rate of consistency is d2 and the calculation cost is O(d3), which might be too expensive in high dimension.

Suggested Citation

  • Kamatani, Kengo, 2020. "Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 297-327.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:297-327
    DOI: 10.1016/j.spa.2019.03.002
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    References listed on IDEAS

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    1. Jarner, Søren Fiig & Hansen, Ernst, 2000. "Geometric ergodicity of Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 341-361, February.
    2. Kengo Kamatani, 2014. "Local consistency of Markov chain Monte Carlo methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 63-74, February.
    3. Søren F. Jarner & Gareth O. Roberts, 2007. "Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 781-815, December.
    4. 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.
    5. 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.
    6. 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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