Scholarlink

<p>This study develops a framework to analyze the convergence of systematic-scan and random-scan Gibbs samplers for bivariate discrete conditional models with possibly different supports. We validate Liu (<i>Test</i>, <b>5</b>, 305-310, 1996)’s conjecture: any stationary distribution of a random-scan Gibbs sampler is a mixture of the stationary distributions of systematic-scan Gibbs samplers. Moreover, we demonstrate the guaranteed convergence of the random-scan Gibbs sampler regardless of the selection probability. This contrasts with the systematic-scan Gibbs sampler, which may fail to converge under different scan orders. Previous studies of the compatibility theory require that the conditional distributions share the same support. By relaxing this requirement, we introduce the concept of generalized compatibility and provide necessary and sufficient conditions for the convergence of systematic-scan and random-scan Gibbs samplers to a unique generalized joint distribution. Furthermore, we establish a link between generalized compatibility and Gibbs sampling and explore the challenges of higher-dimensional extensions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Convergence of systematic-scan and random-scan Gibbs samplers for bivariate discrete conditional distributions

  • 期刊论文

  • 发表日期：

    2026年7月21日

查看全文
  • Sheng-Hsien Chang,
  • Kun-Lin Kuo,
  • Chwan-Chin Song,
  • Thomas J. Jiang

摘要

This study develops a framework to analyze the convergence of systematic-scan and random-scan Gibbs samplers for bivariate discrete conditional models with possibly different supports. We validate Liu (Test, 5, 305-310, 1996)’s conjecture: any stationary distribution of a random-scan Gibbs sampler is a mixture of the stationary distributions of systematic-scan Gibbs samplers. Moreover, we demonstrate the guaranteed convergence of the random-scan Gibbs sampler regardless of the selection probability. This contrasts with the systematic-scan Gibbs sampler, which may fail to converge under different scan orders. Previous studies of the compatibility theory require that the conditional distributions share the same support. By relaxing this requirement, we introduce the concept of generalized compatibility and provide necessary and sufficient conditions for the convergence of systematic-scan and random-scan Gibbs samplers to a unique generalized joint distribution. Furthermore, we establish a link between generalized compatibility and Gibbs sampling and explore the challenges of higher-dimensional extensions.