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不同扫描方式下 Gibbs 采样器的协方差结构与收敛速率AI 解读

SUMMARY This paper presents results on covariance structure and convergence for the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov forward operator and irreducibility of the corresponding chain, the Gibbs sampling scheme converges geometrically in terms of Pearson χ 2-distance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional…

序贯插补与贝叶斯缺失数据问题AI 解读

For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data…

Gibbs 抽样的协方差结构：估计量与数据增广方案的比较AI 解读

We study the covariance structure of a Markov chain generated by the Gibbs sampler, with emphasis on data augmentation. When applied to a Bayesian missing data problem, the Gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector: the empirical distribution based on the sampled values of the parameter vector, and a mixture of complete data posteriors. We prove that Rao-Blackwellization causes a one-lag delay for the…