Convergence properties of the Gibbs sampler for perturbations of Gaussians

• 成果类型: Article
• 署名作者: Amit, Y
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 122-140
• 关键词: stochastic relaxation; bayesian computation; distributions; restoration

摘要

The exact second eigenvalue of the Markov operator of the Gibbs sampler with random sweep strategy for Gaussian densities is calculated, A comparison lemma yields an upper hound on the second eigenvalue for bounded perturbations of Gaussians which is a significant improvement over previous bounds. For two-block Gibbs sampler algorithms with a perturbation of the form chi(g(1)(x((1))) + g(2)(x((2)))) the derivative of the second eigenvalue of the algorithm is calculated exactly at chi = 0, in terms of expectations of the Hessian matrices of g(1) and g(2).