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Gibbs Sampling Methods for StickBreaking Priors
"... ... In this paper we present two general types of Gibbs samplers that can be used to fit posteriors of Bayesian hierarchical models based on stickbreaking priors. The first type of Gibbs sampler, referred to as a Polya urn Gibbs sampler, is a generalized version of a widely used Gibbs sampling meth ..."
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Cited by 213 (17 self)
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... In this paper we present two general types of Gibbs samplers that can be used to fit posteriors of Bayesian hierarchical models based on stickbreaking priors. The first type of Gibbs sampler, referred to as a Polya urn Gibbs sampler, is a generalized version of a widely used Gibbs sampling method currently employed for Dirichlet process computing. This method applies to stickbreaking priors with a known P'olya urn characterization; that is priors with an explicit and simple prediction rule. Our second method, the blocked Gibbs sampler, is based on a 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 as it works without requiring an explicit prediction rule. We find that the blocked Gibbs avoids some of the limitations seen with the Polya urn approach and should be simpler for nonexperts to use.
Hierarchical beta processes and the Indian buffet process. This volume
 In Practical Nonparametric and Semiparametric Bayesian Statistics
, 2007
"... We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving ..."
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Cited by 74 (14 self)
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We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. 1 1
Nonparametric Factor Analysis with Beta Process Priors
"... We propose a nonparametric extension to the factor analysis problem using a beta process prior. This beta process factor analysis (BPFA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observa ..."
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Cited by 37 (16 self)
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We propose a nonparametric extension to the factor analysis problem using a beta process prior. This beta process factor analysis (BPFA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observations. As with the Dirichlet process, the beta process is a fully Bayesian conjugate prior, which allows for analytical posterior calculation and straightforward inference. We derive a variational Bayes inference algorithm and demonstrate the model on the MNIST digits and HGDPCEPH cell line panel datasets. 1.
Poisson process partition calculus with an application to Bayesian . . .
, 2005
"... This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailormade to address inferential questions arising in a wide range of Bayesian nonparametric and spatial statistical models. The P ..."
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Cited by 32 (10 self)
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This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailormade to address inferential questions arising in a wide range of Bayesian nonparametric and spatial statistical models. The Poisson disintegration method is based on the formal statement of two results concerning a Laplace functional change of measure and a Poisson Palm/Fubini calculus in terms of random partitions of the integers {1,...,n}. The techniques are analogous to, but much more general than, techniques for the Dirichlet process and weighted gamma process developed in [Ann. Statist. 12
Semiparametric Bayesian Analysis Of Survival Data
 Journal of the American Statistical Association
, 1996
"... this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics. ..."
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Cited by 23 (0 self)
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this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.
Hierarchical Bayesian Nonparametric Models with Applications ∗
, 2008
"... Hierarchical modeling is a fundamental concept in Bayesian statistics. The basic idea is that parameters are endowed with distributions which may themselves introduce new parameters, and this construction recurses. A common motif in hierarchical modeling is that of the conditionally independent hier ..."
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Cited by 19 (2 self)
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Hierarchical modeling is a fundamental concept in Bayesian statistics. The basic idea is that parameters are endowed with distributions which may themselves introduce new parameters, and this construction recurses. A common motif in hierarchical modeling is that of the conditionally independent hierarchy, in
Sharing Features among Dynamical Systems with Beta Processes
"... We propose a Bayesian nonparametric approach to the problem of modeling related time series. Using a beta process prior, our approach is based on the discovery of a set of latent dynamical behaviors that are shared among multiple time series. The size of the set and the sharing pattern are both infe ..."
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Cited by 19 (6 self)
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We propose a Bayesian nonparametric approach to the problem of modeling related time series. Using a beta process prior, our approach is based on the discovery of a set of latent dynamical behaviors that are shared among multiple time series. The size of the set and the sharing pattern are both inferred from data. We develop an efficient Markov chain Monte Carlo inference method that is based on the Indian buffet process representation of the predictive distribution of the beta process. In particular, our approach uses the sumproduct algorithm to efficiently compute MetropolisHastings acceptance probabilities, and explores new dynamical behaviors via birth/death proposals. We validate our sampling algorithm using several synthetic datasets, and also demonstrate promising results on unsupervised segmentation of visual motion capture data. 1
Consistency issues in Bayesian Nonparametrics
 IN ASYMPTOTICS, NONPARAMETRICS AND TIME SERIES: A TRIBUTE
, 1998
"... ..."
Bayesian estimation of the spectral density of a time series
 J. Amer. Statist. Assoc
, 2004
"... This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updati ..."
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Cited by 15 (3 self)
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This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling from this posterior distribution is described that is used for computing the posterior mean, variance, and other statistics. A consistency result is established for this pseudoposterior distribution that holds for a shortmemory Gaussian time series and under some conditions on the prior. To prove this asymptotic result, a general consistency theorem of Schwartz is extended for a triangular array of independent, nonidentically distributed observations. This extension is also of independent interest. A simulation study is conducted to compare the proposed method with some existing methods. The method is illustrated with the wellstudied sunspot dataset.
Indian Buffet Processes with Powerlaw Behavior
"... The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a threeparameter generalization of the IBP exhibiting powerlaw behavior. We achieve this by generalizing the beta process (the de Finetti me ..."
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Cited by 12 (0 self)
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The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a threeparameter generalization of the IBP exhibiting powerlaw behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the stablebeta process and deriving the IBP corresponding to it. We find interesting relationships between the stablebeta process and the PitmanYor process (another stochastic process used in Bayesian nonparametric models with interesting powerlaw properties). We derive a stickbreaking construction for the stablebeta process, and find that our powerlaw IBP is a good model for word occurrences in document corpora. 1