Approximate Dirichlet process computing in finite normal mixtures: Smoothing and prior information

被引:117
作者
Ishwaran, H
James, LF
机构
[1] Cleveland Clin Fdn, Dept Biostat Wb4, Cleveland, OH 44195 USA
[2] Hong Kong Univ Sci & Technol, Dept Informat & Syst Management, Kowloon, Hong Kong, Peoples R China
关键词
almost sure truncation; blocked Gibbs sampler; nonparanictric hierarchical model; penalized MLE; Polya urn Gibbs sampling; random probability measure;
D O I
10.1198/106186002411
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
A rich nonparametric analysis of the finite normal mixture model is obtained by working with a precise truncation approximation of the Dirichlet process. Model fitting is carried out by a simple Gibbs sampling algorithm that directly samples the nonparametric posterior. The proposed sampler mixes well, requires no tuning parameters, and involves only draws from simple distributions, including the draw for the mass parameter that controls clustering, and the draw for the variances with the use of a nonconjugate uniform prior. Working directly with the nonparametric prior is conceptually appealing and among other things leads to graphical methods for studying the posterior mixing distribution as well as penalized MLE procedures for deriving point estimates. We discuss methods for automating selection of priors for the mean and variance components to avoid over or undersmoothing the data. We also look at the effectiveness of incorporating prior information in die form of frequentist point estimates.
引用
收藏
页码:508 / 532
页数:25
相关论文
共 37 条
[1]  
Akaike H., 1973, 2 INT S INFORM THEOR, P267, DOI [DOI 10.1007/978-1-4612-1694-0_15, 10.1007/978-1-4612-1694-0_15]
[2]  
[Anonymous], PRACTICAL NON PARAME
[3]   A semiparametric Bayesian model for randomised block designs [J].
Bush, CA ;
MacEachern, SN .
BIOMETRIKA, 1996, 83 (02) :275-285
[4]   OPTIMAL RATE OF CONVERGENCE FOR FINITE MIXTURE-MODELS [J].
CHEN, JH .
ANNALS OF STATISTICS, 1995, 23 (01) :221-233
[5]   Marginal likelihood from the Gibbs output [J].
Chib, S .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1995, 90 (432) :1313-1321
[6]  
Devroye L., 1986, NONUNIFORM RANDOM VA
[7]  
DIEBOLT J, 1994, J ROY STAT SOC B MET, V56, P363
[8]   CONTINUITY AND WEAK-CONVERGENCE OF RANKED AND SIZE-BIASED PERMUTATIONS ON THE INFINITE SIMPLEX [J].
DONNELLY, P ;
JOYCE, P .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 31 (01) :89-103
[9]  
Efron B., 1993, INTRO BOOTSTRAP, V1st ed., DOI DOI 10.1201/9780429246593
[10]   BAYESIAN DENSITY-ESTIMATION AND INFERENCE USING MIXTURES [J].
ESCOBAR, MD ;
WEST, M .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1995, 90 (430) :577-588