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

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  • Helali, Amine

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.

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  • Helali, Amine, 2019. "The convergence rate of the Gibbs sampler for generalized 1-D Ising model," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:22
    DOI: 10.1016/j.spl.2019.108555
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    1. Shiu, Shang-Ying & Chen, Ting-Li, 2015. "On the rate of convergence of the Gibbs sampler for the 1-D Ising model by geometric bound," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 14-19.
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