【下载】Bayesian Nonparametrics~J.K.Ghosh.Springer.2003

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Bayesian Nonparametrics (Hardcover)

J.K. Ghosh (Author), R.V. Ramamoorthi (Author)

Editorial Reviews
Review
From the reviews:
"The book will find a place as essential study for researchers in this modern area of statistics. It is well written, the signposts are clearly displayed throughout, and the literature appears to be well documented." ISI Short Book Reviews, Vol. 24/1, Apr. 2004
"This is the first book to present an exhaustive and comprehensive treatment of Bayesian nonparametrics. Ghosh and Ramamoorthi present the theoretical underpinnings of nonparametric priors in a rigorous yet extremely lucid style...It is indispensable to any serious Bayesian. It is bound to become a classic in Bayesian nonparametrics." Sankhya, 2004, Vol. 66, Part 1
"This new monograph by Ghosh and Ramamoorthi fulfills the need for an advanced and complete textbook at the graduate level, dealing with the theoretical aspects of Bayesian nonparametrics and Bayesian asymptotics. This is a noteworthy book that covers, with mathematical rigor, a broad class of subjects...Bayesian Nonparametrics will give researchers in the area of nonparametric and semiparametric Bayesian inference a well-written introduction to the theoretical aspects of the discipline, and it should be considered a must for anyone interested in Bayesian asymptotics." Journal of the American Statistical Association, September 2004
"This is the first book to present an exhaustive and comprehensive treatment of Bayesian nonparametrics. Ghosh and Ramamoorthi present the theoretical underpinnings of nonparametric priors in a rigourous yet extremely lucid style. … It is an excellent book for a serious reader … . This book is unique in doing all this in an elegant way – the proofs are all presented in an eminently readable style. It is indispensable to any serious Bayesian. It is bound to become a classic in Bayesian nonparametrics." (Jayaram Sethuraman, Sankhya: The Indian Journal of Statistics, Vol. 66 (1), 2004)
"The style of the book is well summarized in the following quotations: ‘This monograph provides a systematic, theoretical development of the subject’. … The book will find a place as essential study for researches in this modern area of statistics. It is well written, the signposts are clearly displayed throughout, and the literature appears to be well documented." (M. J. Crowder, Short Book Reviews, Vol. 24 (1), 2004)
"The present monograph gives a nice overview on the state of the art in Bayesian nonparametrics. … The reader will find a huge amount of references. In conclusion, the present book can be recommended for research and advanced lectures and seminars." (Arnold Janssen, Zentralblatt MATH, Vol. 1029, 2004)
"Nonparametrics and other infinite-dimensional problems have been difficult for Bayesians to deal with for various reasons. … In view of all these formidable difficulties, the advances achieved in this field in recent years are truly remarkable. The book by Ghosh and Ramamoorthi discusses theoretical aspects of these advances in Bayesian nonparametrics and Bayesian asymptotics. … The book is suggested as an introductory text at the graduate level. … It can also serve as an excellent reference book for researchers." (Mohan Delampady, Mathematical Reviews, 2004g)
Product Description
Bayesian 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.


Product Details

• Hardcover: 304 pages
• Publisher: Springer; 1 edition (April 8, 2003)
• Language: English
• ISBN-10: 0387955372
• ISBN-13: 978-0387955377

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关键词：Parametric Springer Bayesian nonpara metrics 下载 Bayesian Springer ghosh

Contents

Introduction:Why Bayesian Nonparametrics—An Overview and Summary 1

1 Preliminaries and the Finite Dimensional Case 9

1.1 Introduction 9

1.2 Metric Spaces 10

1.2.1 preliminaries 10

1.2.2 Weak Convergence 12

1.3 Posterior Distribution and Consistency 15

1.3.1 Preliminaries 15

1.3.2 Posterior Consistency and Posterior Robustness 18

1.3.3 Doob’s Theorem 22

1.3.4 Wald-Type Conditions 24

1.4 Asymptotic Normality of MLE and
Bernstein–von Mises Theorem 33

1.5 Ibragimov and Hasminski˘ı Conditions 41

1.6 Nonsubjective Priors 46

1.6.1 Fully Specified 46

1.6.2 Discussion 52

1.7 Conjugate and Hierarchical Priors 52

1.8 Exchangeability, De Finetti’s Theorem,

Exponential Families 54

2 M(X) and Priors on M(X) 57

2.1 Introduction 57

2.2 The Space M(X) 58

2.3 (Prior) Probability Measures on M(X) 62

2.3.1 X Finite 62

2.3.2 X = R 64

2.3.3 Tail Free Priors 70

2.4 Tail Free Priors and 0-1 Laws 75

2.5 Space of Probability Measures on M(R) 78

2.6 De Finetti’s Theorem 83

3 Dirichlet and Polya tree process 87

3.1 Dirichlet and Polya tree process 87

3.1.1 Finite Dimensional Dirichlet Distribution 87

3.1.2 Dirichlet Distribution via Polya Urn Scheme 94

3.2 Dirichlet Process on M(R) 96

3.2.1 Construction and Properties 96

3.2.2 The Sethuraman Construction 103

3.2.3 Support of Dα 104

3.2.4 Convergence Properties of Dα 105

3.2.5 Elicitation and Some Applications 107

3.2.6 Mutual Singularity of Dirichlet Priors 110

3.2.7 Mixtures of Dirichlet Process 113

3.3 Polya Tree Process 114

3.3.1 The Finite Case 114

3.3.2 X = R 116

4 Consistency Theorems 121

4.1 Introduction 121

4.2 Preliminaries 122

4.3 Finite and Tail free case 124

4.4 Posterior Consistency on Densities 126

4.4.1 Schwartz Theorem 126

4.4.2 L1-Consistency 132

4.5 Consistency via LeCam’s inequality 137

5 Density Estimation 141

5.1 Introduction 141

5.2 Polya Tree Priors 142

5.3 Mixtures of Kernels 143

5.4 Hierarchical Mixtures 147

5.5 RandomHistograms 148

5.5.1 Weak Consistency 150

5.5.2 L1-Consistency 156

5.6 Mixtures of Normal Kernel 161

5.6.1 DirichletMixtures:Weak Consistency 161

5.6.2 Dirichlet Mixtures: L1-Consistency 169

5.6.3 Extensions 172

5.7 Gaussian Process Priors 174

6 Inference for Location Parameter 181

6.1 Introduction 181

6.2 The Diaconis-Freedman Example 182

6.3 Consistency of the Posterior 185

6.4 Polya Tree Priors 189

7 Regression Problems 197

7.1 Introduction 197

7.2 Schwartz Theorem 198

7.3 Exponentially Consistent Tests 201

7.4 Prior Positivity of Neighborhoods 206

7.5 Polya Tree Priors 208

7.6 Dirichlet Mixture of Normals 209

7.7 Binary Response Regression with Unknown Link 212

7.8 Stochastic Regressor 215

7.9 Simulations 215

8 Uniform Distribution on Infinite-Dimensional Spaces 221

8.1 Introduction 221

8.2 Towards a Uniform Distribution 222

8.2.1 The Jeffreys Prior 222

8.2.2 Uniform Distribution via Sieves and Packing Numbers 223

8.3 Technical Preliminaries 224

8.4 The Jeffreys Prior Revisited 225

8.5 Posterior Consistency for Noninformative Priors for
Infinite-Dimensional Problems 229

8.6 Convergence of Posterior at Optimal Rate 231

9 Survival Analysis—Dirichlet Priors 237

9.1 Introduction 237

9.2 Dirichlet Prior 238

9.3 Cumulative Hazard Function, Identifiability 242

9.4 Priors via Distributions of (Z, δ) 247

9.5 Interval Censored Data 249

10 Neutral to the Right Priors 253

10.1 Introduction 253

10.2 Neutral to the Right Priors 254

10.3 Independent Increment Processes 258

10.4 Basic Properties 262

10.5 Beta Processes 265

10.5.1 Definition and Construction 265

10.5.2 Properties 268

10.6 Posterior Consistency 271

11 Exercises 281

References 285

Index 300

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