Gibbs Sampling Methods for Stick-Breaking Priorsстатья из журнала
Аннотация: AbstractA rich and flexible class of random probability measures, which we call stick-breaking priors, can be constructed using a sequence of independent beta random variables. Examples of random measures that have this characterization include the Dirichlet process, its two-parameter extension, the two-parameter Poisson–Dirichlet process, finite dimensional Dirichlet priors, and beta two-parameter processes. The rich nature of stick-breaking priors offers Bayesians a useful class of priors for nonparametric problems, while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them. In this article we present two general types of Gibbs samplers that can be used to fit posteriors of Bayesian hierarchical models based on stick-breaking priors. The first type of Gibbs sampler, referred to as a Pólya urn Gibbs sampler, is a generalized version of a widely used Gibbs sampling method currently employed for Dirichlet process computing. This method applies to stick-breaking priors with a known Pólya urn characterization, that is, priors with an explicit and simple prediction rule. Our second method, the blocked Gibbs sampler, is based on an entirely different approach that works by directly sampling values from the posterior of the random measure. The blocked Gibbs sampler can be viewed as a more general approach because it works without requiring an explicit prediction rule. We find that the blocked Gibbs avoids some of the limitations seen with the Pólya urn approach and should be simpler for nonexperts to use.KEY WORDS: Blocked Gibbs samplerDirichlet processGeneralized Dirichlet distributionPitman–Yor processPólya urn Gibbs samplerPrediction ruleRandom probability measureRandom weightsStable law
Год издания: 2001
Авторы: Hemant Ishwaran, Lancelot F. James
Источник: Journal of the American Statistical Association
Ключевые слова: Bayesian Methods and Mixture Models, Markov Chains and Monte Carlo Methods, Stochastic processes and statistical mechanics
Открытый доступ: closed
Том: 96
Выпуск: 453
Страницы: 161–173