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Ergodicity of Markov chain Monte Carlo with reversible proposal

  • K. Kamatani (a1)
Abstract
Abstract

We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

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* Postal address: Graduate School of Engineering Science and Center for Mathematical Modeling and Data Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan. Email address: kamatani@sigmath.es.osaka-u.ac.jp
References
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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