Holdings: Bayesian nonparametrics

Bayesian nonparametrics:

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Bibliographic Details
Main Authors:	Ghosh, Jayanta K. (Author), Ramamoorthi, R. V. (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 2003
Subjects:	Besliskunde Inferência bayesiana (inferência estatística) Methode van Bayes Non-parametrische statistiek Bayesian statistical decision theory Nonparametric statistics Bayes-Entscheidungstheorie Nichtparametrisches Verfahren
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 285 - 299
Physical Description:	XII, 305 S.
ISBN:	0387955372

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adam_text	CONTENTS INTRODUCTION: WHY BAYESIAN NONPARAMETRICSAN OVERVIEW AND SUM- MARY 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 DOOBS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.4 WALD-TYPE CONDITIONS . . . . . . . . . . . . . . . . . . . . . . 24 1.4 ASYMPTOTIC NORMALITY OF MLE AND BERNSTEINVON MISES THEOREM . . . . . . . . . . . . . . . . . . . . . . 33 1.5 IBRAGIMOV AND HASMINSKI * 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 X CONTENTS 1.8 EXCHANGEABILITY, DE FINETTIS 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 FINETTIS 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 D * . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.2.4 CONVERGENCE PROPERTIES OF D * . . . . . . . . . . . . . . . . . . 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 L 1 -CONSISTENCY . . . . . . . . . . . . . . . . . . . . . . . . . . 132 CONTENTS XI 4.5 CONSISTENCY VIA LECAMS 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 RANDOM HISTOGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.5.1 WEAK CONSISTENCY . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.5.2 L 1 -CONSISTENCY . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.6 MIXTURES OF NORMAL KERNEL . . . . . . . . . . . . . . . . . . . . . . . . 161 5.6.1 DIRICHLET MIXTURES: WEAK CONSISTENCY . . . . . . . . . . . . . . 161 5.6.2 DIRICHLET MIXTURES: L 1 -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 XII CONTENTS 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 ANALYSISDIRICHLET 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, * ) . . . . . . . . . . . . . . . . . . . . . 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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spelling	Ghosh, Jayanta K. Verfasser aut Bayesian nonparametrics J. K. Ghosh ; R. V. Ramamoorthi New York [u.a.] Springer 2003 XII, 305 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 285 - 299 Besliskunde gtt Inferência bayesiana (inferência estatística) larpcal Methode van Bayes gtt Non-parametrische statistiek gtt Bayesian statistical decision theory Nonparametric statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Nichtparametrisches Verfahren (DE-588)4339273-8 s DE-604 Ramamoorthi, R. V. Verfasser (DE-588)124691943 aut SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010376715&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ghosh, Jayanta K. Ramamoorthi, R. V. Bayesian nonparametrics Besliskunde gtt Inferência bayesiana (inferência estatística) larpcal Methode van Bayes gtt Non-parametrische statistiek gtt Bayesian statistical decision theory Nonparametric statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd
subject_GND	(DE-588)4144220-9 (DE-588)4339273-8
title	Bayesian nonparametrics
title_auth	Bayesian nonparametrics
title_exact_search	Bayesian nonparametrics
title_full	Bayesian nonparametrics J. K. Ghosh ; R. V. Ramamoorthi
title_fullStr	Bayesian nonparametrics J. K. Ghosh ; R. V. Ramamoorthi
title_full_unstemmed	Bayesian nonparametrics J. K. Ghosh ; R. V. Ramamoorthi
title_short	Bayesian nonparametrics
title_sort	bayesian nonparametrics
topic	Besliskunde gtt Inferência bayesiana (inferência estatística) larpcal Methode van Bayes gtt Non-parametrische statistiek gtt Bayesian statistical decision theory Nonparametric statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd
topic_facet	Besliskunde Inferência bayesiana (inferência estatística) Methode van Bayes Non-parametrische statistiek Bayesian statistical decision theory Nonparametric statistics Bayes-Entscheidungstheorie Nichtparametrisches Verfahren
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010376715&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT ghoshjayantak bayesiannonparametrics AT ramamoorthirv bayesiannonparametrics

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