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

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.