Convergence rate of Gibbs sampler and its application  

作　　者：LI Kaican GENG Zhi 

机构地区：[1]Department of Mathematics, Hubei Normal University, Huangshi 435002, China [2]LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

出　　处：《Science China Mathematics》2005年第10期1430-1439,共10页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10431010);National Basic Research Project,973(Grant No.2003CB715900).

摘　　要：Based on the convergence rate defined by the Pearson-χ~2 distance,this pa- per 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 sam- pler 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.Based on the convergence rate defined by the Pearson-x2 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-x2 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.

关 键 词：compact operator Gibbs samplers Hilbert space transition function DOI:10. 1360/02ys0013 

分 类 号：N[自然科学总论]