Dependent mixtures of geometric weights priors

A new approach to the joint estimation of partially exchangeable observations is presented. This is achieved by constructing a model with pairwise dependence between random density functions, each of which is modeled as a mixture of geometric stick breaking processes. The main contention is that mixture modeling with Pairwise Dependent Geometric Stick Breaking Process (PDGSBP) priors is sufficient for prediction and estimation purposes; that is, making the weights more exotic does not actually enlarge the support of the prior. Moreover, the corresponding Gibbs sampler for estimation is faster and easier to implement than the Dirichlet Process counterpart.

[1]  Stephen G. Walker,et al.  A Bayesian nonparametric estimator of a multivariate survival function , 2009 .

[2]  D. Dunson,et al.  Kernel stick-breaking processes. , 2008, Biometrika.

[3]  M. Steel,et al.  Comparing distributions by using dependent normalized random‐measure mixtures , 2013 .

[4]  S. MacEachern,et al.  An ANOVA Model for Dependent Random Measures , 2004 .

[5]  Stephen G. Walker,et al.  Sampling the Dirichlet Mixture Model with Slices , 2006, Commun. Stat. Simul. Comput..

[6]  S. MacEachern.  Decision Theoretic Aspects of Dependent Nonparametric Processes , 2000 .

[7]  Antonio Lijoi,et al.  Dependent mixture models: Clustering and borrowing information , 2014, Comput. Stat. Data Anal..

[8]  M. West,et al.  Hyperparameter estimation in Dirichlet process mixture models , 1992 .

[9]  Stephen G. Walker,et al.  A nonparametric dependent process for Bayesian regression , 2009 .

[10]  Michael,et al.  On a Class of Bayesian Nonparametric Estimates : I . Density Estimates , 2008 .

[11]  Stephen G. Walker,et al.  Random density functions with common atoms and pairwise dependence , 2015, Comput. Stat. Data Anal..

[12]  Jim E. Griffin,et al.  On Bayesian nonparametric modelling of two correlated distributions , 2013, Stat. Comput..

[13]  Stephen G. Walker,et al.  A New Bayesian Nonparametric Mixture Model , 2010, Commun. Stat. Simul. Comput..

[14]  J. Sethuraman.  A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS , 1991 .

[15]  Stephen G. Walker,et al.  Dependent mixtures of Dirichlet processes , 2011, Comput. Stat. Data Anal..

[16]  J. E. Griffin,et al.  Order-Based Dependent Dirichlet Processes , 2006 .

[17]  Ramsés H. Mena,et al.  Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling , 2011 .

[18]  A. Lijoi,et al.  Bayesian inference with dependent normalized completely random measures , 2014, 1407.0482.

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

[20]  Stephen G. Walker,et al.  Bayesian nonparametric density estimation under length bias , 2015, Commun. Stat. Simul. Comput..

[21]  P. Müller,et al.  A method for combining inference across related nonparametric Bayesian models , 2004 .