
At a Glance
324 Pages
23.5 x 15.88 x 1.91
Hardcover
$299.00
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Industry Reviews
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 wellsummarized 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)
| Introduction: Why Bayesian Nonparametrics-An Overview and Sum-mary | p. 1 |
| Preliminaries and the Finite Dimensional Case | p. 9 |
| Introduction | p. 9 |
| Metric Spaces | p. 10 |
| preliminaries | p. 10 |
| Weak Convergence | p. 12 |
| Posterior Distribution and Consistency | p. 15 |
| Preliminaries | p. 15 |
| Posterior Consistency and Posterior Robustness | p. 18 |
| Doob's Theorem | p. 22 |
| Wald-Type Conditions | p. 24 |
| Asymptotic Normality of MLE and Bernstein-von Mises Theorem | p. 33 |
| Ibragimov and Hasminski&ibreve; Conditions | p. 41 |
| Nonsubjective Priors | p. 46 |
| Fully Specified | p. 46 |
| Discussion | p. 52 |
| Conjugate and Hierarchical Priors | p. 52 |
| Exchangeability, De Finetti's Theorem, Exponential Families | p. 54 |
| <$>M({\cal X})<$> and Priors on <$>M({\cal X})<$> | p. 57 |
| Introduction | p. 57 |
| The Space M(X) | p. 58 |
| (Prior) Probability Measures on <$>M({\cal X})<$> | p. 62 |
| <$>{\cal X}<$> Finite | p. 62 |
| <$>{\cal X} = {\op R}<$> | p. 64 |
| Tail Free Priors | p. 70 |
| Tail Free Priors and 0-1 Laws | p. 75 |
| Space of Probability Measures on <$>M({\op R})<$> | p. 78 |
| De Finetti's Theorem | p. 83 |
| Dirichlet and Polya tree process | p. 87 |
| Dirichlet and Polya tree process | p. 87 |
| Finite Dimensional Dirichlet Distribution | p. 87 |
| Dirichlet Distribution via Polya Urn Scheme | p. 94 |
| Dirichlet Process on <$>M({\op R})<$> | p. 96 |
| Construction and Properties | p. 96 |
| The Sethuraman Construction | p. 103 |
| Support of D¿ | p. 104 |
| Convergence Properties of D¿ | p. 105 |
| Elicitation and Some Applications | p. 107 |
| Mutual Singularity of Dirichlet Priors | p. 110 |
| Mixtures of Dirichlet Process | p. 113 |
| Polya Tree Process | p. 114 |
| The Finite Case | p. 114 |
| <$>{\cal X} = {\op R}<$> | p. 116 |
| Consistency Theorems | p. 121 |
| Introduction | p. 121 |
| Preliminaries | p. 122 |
| Finite and Tail free case | p. 124 |
| Posterior Consistency on Densities | p. 126 |
| Schwartz Theorem | p. 126 |
| L1-Consistency | p. 132 |
| Consistency via LeCam's inequality | p. 137 |
| Density Estimation | p. 141 |
| Introduction | p. 141 |
| Polya Tree Priors | p. 142 |
| Mixtures of Kernels | p. 143 |
| Hierarchical Mixtures | p. 147 |
| Random Histograms | p. 148 |
| Weak Consistency | p. 150 |
| L1-Consistency | p. 156 |
| Mixtures of Normal Kernel | p. 161 |
| Dirichlet Mixtures: Weak Consistency | p. 161 |
| Dirichlet Mixtures: L1-Consistency | p. 169 |
| Extensions | p. 172 |
| Gaussian Process Priors | p. 174 |
| Inference for Location Parameter | p. 181 |
| Introduction | p. 181 |
| The Diaconis-Freedman Example | p. 182 |
| Consistency of the Posterior | p. 185 |
| Polya Tree Priors | p. 189 |
| Regression Problems | p. 197 |
| Introduction | p. 197 |
| Schwartz Theorem | p. 198 |
| Exponentially Consistent Tests | p. 201 |
| Prior Positivity of Neighborhoods | p. 206 |
| Polya Tree Priors | p. 208 |
| Dirichlet Mixture of Normals | p. 209 |
| Binary Response Regression with Unknown Link | p. 212 |
| Stochastic Regressor | p. 215 |
| Simulations | p. 215 |
| Uniform Distribution on Infinite-Dimensional Spaces | p. 221 |
| Introduction | p. 221 |
| Towards a Uniform Distribution | p. 222 |
| The Jeffreys Prior | p. 222 |
| Uniform Distribution via Sieves and Packing Numbers | p. 223 |
| Technical Preliminaries | p. 224 |
| The Jeffreys Prior Revisited | p. 225 |
| Posterior Consistency for Noninformative Priors for Infinite-Dimensional Problems | p. 229 |
| Convergence of Posterior at Optimal Rate | p. 231 |
| Survival Analysis-Dirichlet Priors | p. 237 |
| Introduction | p. 237 |
| Dirichlet Prior | p. 238 |
| Cumulative Hazard Function, Identifiability | p. 242 |
| Priors via Distributions of (Z, ¿) | p. 247 |
| Interval Censored Data | p. 249 |
| Neutral to the Right Priors | p. 253 |
| Introduction | p. 253 |
| Neutral to the Right Priors | p. 254 |
| Independent Increment Processes | p. 258 |
| Basic Properties | p. 262 |
| Beta Processes | p. 265 |
| Definition and Construction | p. 265 |
| Properties | p. 268 |
| Posterior Consistency | p. 271 |
| Exercises | p. 281 |
| References | p. 285 |
| Index | p. 300 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780387955377
ISBN-10: 0387955372
Series: Springer Series in Statistics
Published: 8th April 2003
Format: Hardcover
Language: English
Number of Pages: 324
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 23.5 x 15.88 x 1.91
Weight (kg): 0.58
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