The convergence rate of the Gibbs sampler for generalized 1-D Ising model

Amine Helali

Statistics & Probability Letters, 2019, vol. 154, issue C, -

Abstract: The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by β∗. In this paper we generalize a bound for β∗ from Shiu and Chen (2015) for the one-dimensional Ising model with two states to a multiple state situation. The method is based on Diaconis and Stroock bound for reversible Markov processes. The new bound presented in this paper improves Ingrassia’s (1994) result.

Keywords: Markov chain Monte Carlo; Rate of convergence; Gibbs sampler; Ising model (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.108555

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