- Volume 24, Number 4B (2018), 3711-3750.
Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution
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.
Bernoulli, Volume 24, Number 4B (2018), 3711-3750.
Received: January 2015
Revised: March 2017
First available in Project Euclid: 18 April 2018
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Kamatani, Kengo. Efficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distribution. Bernoulli 24 (2018), no. 4B, 3711--3750. doi:10.3150/17-BEJ976. https://projecteuclid.org/euclid.bj/1524038768