Premium
A method for combining inference across related nonparametric Bayesian models
Author(s) -
Müller Peter,
Quintana Fernando,
Rosner Gary
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2004.05564.x
Subject(s) - dirichlet process , hierarchical dirichlet process , nonparametric statistics , markov chain monte carlo , inference , computer science , context (archaeology) , hierarchical database model , bayesian inference , bayes' theorem , dirichlet distribution , parametric statistics , bayesian probability , mathematics , artificial intelligence , econometrics , data mining , latent dirichlet allocation , statistics , topic model , paleontology , mathematical analysis , biology , boundary value problem
Summary. We consider the problem of combining inference in related nonparametric Bayes models. Analogous to parametric hierarchical models, the hierarchical extension formalizes borrowing strength across the related submodels. In the nonparametric context, modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional. We discuss a formal definition of such a hierarchical model. The approach includes a regression at the level of the nonparametric model. For the special case of Dirichlet process mixtures, we develop a Markov chain Monte Carlo scheme to allow efficient implementation of full posterior inference in the given model.