## Bayesian NonparametricsBayesian nonparametrics has grown tremendously in the last three decades, especially in the last few years. This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. While the book is of special interest to Bayesians, it will also appeal to statisticians in general because Bayesian nonparametrics offers a whole continuous spectrum of robust alternatives to purely parametric and purely nonparametric methods of classical statistics. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian nonparametrics. Though the emphasis of the book is on nonparametrics, there is a substantial chapter on asymptotics of classical Bayesian parametric models. Jayanta Ghosh has been Director and Jawaharlal Nehru Professor at the Indian Statistical Institute and President of the International Statistical Institute. He is currently professor of statistics at Purdue University. He has been editor of Sankhya and served on the editorial boards of several journals including the Annals of Statistics. Apart from Bayesian analysis, his interests include asymptotics, stochastic modeling, high dimensional model selection, reliability and survival analysis and bioinformatics. R.V. Ramamoorthi is professor at the Department of Statistics and Probability at Michigan State University. He has published papers in the areas of sufficiency invariance, comparison of experiments, nonparametric survival analysis and Bayesian analysis. In addition to Bayesian nonparametrics, he is currently interested in Bayesian networks and graphical models. He is on the editorial board of Sankhya. |

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### Contents

Why Bayesian NonparametricsAn Overview and Sum | 1 |

Density Estimation | 5 |

Survival AnalysisDirichlet Priors | 9 |

1 | 56 |

5 | 73 |

Neutral to the Right Priors | 74 |

6 | 83 |

2 | 90 |

Consistency Theorems | 121 |

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### Common terms and phrases

assumption asymptotic Bayes estimate Bayesian Borel sets censored Chapter compact condition conjugate priors consider construction continuous converges weakly corresponding countable deﬁned Deﬁnition denote density estimation Dirichlet distribution Dirichlet mixtures Dirichlet prior Dirichlet process discrete discussed distribution function example exists Finetti’s theorem ﬁnite finite-dimensional ﬁrst follows g G E Ghosh given X1 X2 Hellinger distance hence histogram independent increment process integral Jeffreys prior joint distribution K-L support Kullback-Leibler Lebesgue measure Lemma likelihood marginal distribution metric space mixture of normal neutral noninformative nonparametric nonsubjective prior observations open sets partition Polya tree priors posterior consistency posterior distribution posterior given probability measure problems Proof Proposition random variables Remark result right priors satisﬁes Schwartz Schwartz’s theorem separable metric space sequence Statist subset Suppose tail free priors total variation weak convergence weakly consistent