Nils Lid Hjort, Chris Holmes, Peter Müller, Stephen G. Walker
Cambridge University Press, Apr 12, 2010 - Mathematics
Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.
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motivation and ideas
2 The Dirichlet process related priors and posterior asymptotics
3 Models beyond the Dirichlet process
4 Further models and applications
5 Hierarchical Bayesian nonparametric models with applications
Other editions - View all
algorithm American Statistical Association analysis Annals of Statistics applications approach atoms base measure Bayes estimates Bayes factor Bayesian inference Bayesian nonparametric beta process Chapter components computational conditional consider consistency construction corresponding covariance deﬁned deﬁnition denote density estimation difﬁcult Dirichlet distribution Dirichlet process discrete discussion DP prior Dunson example ﬁnite ﬁrst ﬁxed ﬂexible frequentist Gaussian process Ghahramani Ghosal Gibbs sampler given HDP-HMM hierarchical models Hjort independent inﬁnite inﬁnite-dimensional Jordan Journal Kullback–Leibler L´evy intensity latent variables Lijoi M¨uller Markov MCMC methods mixture model nonparametric Bayes nonparametric Bayesian nonparametric models nonparametric priors normal NRMI number of clusters observations P´olya tree parameters parametric model partition Pitman Pitman–Yor process posterior distribution posterior probability Pr¨unster predictors prior distribution probability measure problem random effects random measures random probability measure random variables regression sampling Section semiparametric sequence simulation speciﬁc updated values Walker weights