Abstract
Based on the convergence rate defined by the Pearson– χ 2 distance, this paper discusses properties of different Gibbs sampling schemes. Under a set of regularity conditions, it is proved in this paper that the rate of convergence on systematic scan Gibbs samplers is the norm of a forward operator. We also discuss that the collapsed Gibbs sampler has a faster convergence rate than the systematic scan Gibbs sampler as proposed by Liu et al. Based on the definition of convergence rate of the Pearson– χ 2 distance, this paper proved this result quantitatively. According to Theorem 2, we also proved that the convergence rate defined with the spectral radius of matrix by Robert and Shau is equivalent to the corresponding radius of the forward operator.
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