Computational Methods for Mixture of Dirichlet Process Models

This chapter lays out the basic computational strategies for models based on mixtures of Dirichlet processes. I describe the basic algorithm and give advice on how to improve this algorithm through a collapse of the state space of the Markov chain and through blocking of variates for generation. The computational methods are illustrated with a beta-binomial example and with the bioassay problem. Some advice is given for dealing with models that have little or no conjugacy present.

[1]  W. Dixon.  The Up-and-Down Method for Small Samples , 1965 .

[2]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[3]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[4]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[5]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[6]  B. Efron,et al.  Data Analysis Using Stein's Estimator and its Generalizations , 1975 .

[7]  L. Kuo.  Bayesian Bioassay Design , 1983 .

[8]  L. Kuo.  Computations of mixtures of dirichlet processes , 1986 .

[9]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[10]  A. Gelfand,et al.  Nonparametric Bayesian bioassay including ordered polytomous response , 1991 .

[11]  Lynn Kuo,et al.  Bayesian Computations in Survival Models via the Gibbs Sampler , 1992 .

[12]  Related Topics,et al.  Survival analysis : state of the art , 1992 .

[13]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[14]  Hani Doss.  Bayesian Nonparametric Estimation for Incomplete Data Via Successive Substitution Sampling , 1994 .

[15]  Christopher A. Bush.  Semi-parametric Bayesian linear models / , 1994 .

[16]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[17]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .

[18]  Jun S. Liu,et al.  The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene Regulation Problem , 1994 .

[19]  S. MacEachern.  Estimating normal means with a conjugate style dirichlet process prior , 1994 .

[20]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[21]  M. Newton,et al.  Bayesian Inference for Semiparametric Binary Regression , 1996 .

[22]  P. Müller,et al.  Bayesian curve fitting using multivariate normal mixtures , 1996 .

[23]  S. MacEachern,et al.  A semiparametric Bayesian model for randomised block designs , 1996 .

[24]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[25]  M. Evans,et al.  Random Variable Generation Using Concavity Properties of Transformed Densities , 1998 .

[26]  Jun S. Liu,et al.  Sequential importance sampling for nonparametric Bayes models: The next generation , 1999 .