Models beyond the Dirichlet process
Antonio Lijoi,Igor Prünster +1 more
TL;DR: In this paper, the authors provide a review of Bayesian nonparametric models that go beyond the Dirichlet process, and show that in some cases of interest for statistical applications, the DPM is not an adequate prior choice.
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Abstract: Bayesian nonparametric inference is a relatively young area of research and it has recently undergone a strong development. Most of its success can be explained by the considerable degree of exibility it ensures in statistical modelling, if compared to parametric alternatives, and by the emergence of new and ecient simulation techniques that make nonparametric models amenable to concrete use in a number of applied statistical problems. Since its introduction in 1973 by T.S. Ferguson, the Dirichlet process has emerged as a cornerstone in Bayesian nonparametrics. Nonetheless, in some cases of interest for statistical applications the Dirichlet process is not an adequate prior choice and alternative nonparametric models need to be devised. In this paper we provide a review of Bayesian nonparametric models that go beyond the Dirichlet process.
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TL;DR: This chapter discusses nonparametric statistical models, function spaces and approximation theory, and the minimax paradigm, which aims to provide a model for adaptive inference oflihood-based procedures.
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TL;DR: The most commonly used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in high-dimensional spaces as discussed by the authors.
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Bayesian Nonparametric Inference – Why and How
Peter Müller,Riten Mitra +1 more
TL;DR: Inference under models with nonparametric Bayesian (BNP) priors is reviewed for density estimation, clustering, regression and for mixed effects models with random effects distributions.
•Posted Content
Mixture models with a prior on the number of components
TL;DR: It turns out that many of the essential properties of DPMs are also exhibited by MFMs, and the MFM analogues are simple enough that they can be used much like the corresponding DPM properties; this simplifies the implementation of MFMs and can substantially improve mixing.
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References
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The annual report.
TL;DR: Service-learning is a form of structured experiential education in which students engage with the community to be active learners, to enrich their sense of civic responsibility, and to explore practical application for course content.
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A Bayesian Analysis of Some Nonparametric Problems
TL;DR: In this article, a class of prior distributions, called Dirichlet process priors, is proposed for nonparametric problems, for which treatment of many non-parametric statistical problems may be carried out, yielding results that are comparable to the classical theory.
Bayesian Density Estimation and Inference Using Mixtures
Michael Escobar,Mike West +1 more
TL;DR: In this article, the authors describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes and show convergence results for a general class of normal mixture models.
2.6K
Markov Chain Sampling Methods for Dirichlet Process Mixture Models
TL;DR: In this article, Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model are presented, and two new classes of methods are presented. But neither of these methods is suitable for handling general models with non-conjugate priors.
2.6K