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November 2018 Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution
Kengo Kamatani
Bernoulli 24(4B): 3711-3750 (November 2018). DOI: 10.3150/17-BEJ976

Abstract

The purpose of this paper is to introduce a new Markov chain Monte Carlo method and to express its effectiveness by simulation and high-dimensional asymptotic theory. The key fact is that our algorithm has a reversible proposal kernel, which is designed to have a heavy-tailed invariant probability distribution. A high-dimensional asymptotic theory is studied for a class of heavy-tailed target probability distributions. When the number of dimensions of the state space passes to infinity, we will show that our algorithm has a much higher convergence rate than the pre-conditioned Crank–Nicolson (pCN) algorithm and the random-walk Metropolis algorithm.

Citation

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Kengo Kamatani. "Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution." Bernoulli 24 (4B) 3711 - 3750, November 2018. https://doi.org/10.3150/17-BEJ976

Information

Received: 1 January 2015; Revised: 1 March 2017; Published: November 2018
First available in Project Euclid: 18 April 2018

zbMATH: 06869890
MathSciNet: MR3788187
Digital Object Identifier: 10.3150/17-BEJ976

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 4B • November 2018
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