Multivariate Bayesian statistics: models for source separation and signal unmixing
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
Chapman & Hall/CRC
2003
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 329 S. graph. Darst. |
| ISBN: | 1584883189 |
Staff View
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| adam_text | MULTIVARIATE BAYESIAN STATISTICS MODELS FOR SOURCE SEPARATION AND SIGNAL
UNMIXING DANIEL B. ROWE CHAPMAN & HALL/CRC A CRC PRESS COMPANY BOCA
RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS LIST OF FIGURES XVII
LIST OF TABLES XIX 1 INTRODUCTION 1 1.1 THE COCKTAIL PARTY 1 1.2 THE
SOURCE SEPARATION MODEL 2 1 FUNDAMENTALS 9 2 STATISTICAL DISTRIBUTIONS
11 2.1 SCALAR DISTRIBUTIONS 11 2.1.1 BINOMIAL 11 2.1.2 BETA 12 2.1.3
NORMAL 14 2.1.4 GAMMA AND SCALAR WISHART 14 2.1.5 INVERTED GAMMA AND
SCALAR INVERTED WISHART . . . . 16 2.1.6 STUDENT T 17 2.1.7
F-DISTRIBUTION 19 2.2 VECTOR DISTRIBUTIONS 20 2.2.1 MULTIVARIATE NORMAL
20 2.2.2 MULTIVARIATE STUDENT T 20 2.3 MATRIX DISTRIBUTIONS 22 2.3.1
MATRIX NORMAL 22 2.3.2 WISHART 24 2.3.3 INVERTED WISHART 25 2.3.4 MATRIX
T 26 3 INTRODUCTORY BAYESIAN STATISTICS 31 3.1 DISCRETE SCALAR VARIABLES
31 3.1.1 BAYES RULE AND TWO SIMPLE EVENTS 31 3.1.2 BAYES RULE AND THE
LAW OF TOTAL PROBABILITY . . . . 32 3.2 CONTINUOUS SCALAR VARIABLES 34
3.3 CONTINUOUS VECTOR VARIABLES 36 3.4 CONTINUOUS MATRIX VARIABLES 37 XI
XLL 4 PRIOR DISTRIBUTIONS 41 4.1 VAGUE PRIORS 41 4.1.1 SCALAR VARIATES
41 4.1.2 VECTOR VARIATES 43 4.1.3 MATRIX VARIATES 43 4.2 CONJUGATE
PRIORS 43 4.2.1 SCALAR VARIATES 44 4.2.2 VECTOR VARIATES 45 4.2.3 MATRIX
VARIATES 47 4.3 GENERALIZED PRIORS 48 4.3.1 SCALAR VARIATES 48 4.3.2
VECTOR VARIATES 49 4.3.3 MATRIX VARIATES 51 4.4 CORRELATION PRIORS 52
4.4.1 INTRACLASS 53 4.4.2 MARKOV 54 5 HYPERPARAMETER ASSESSMENT 59 5.1
INTRODUCTION 59 5.2 BINOMIAL LIKELIHOOD 59 5.2.1 SCALAR BETA 60 5.3
SCALAR NORMAL LIKELIHOOD 60 5.3.1 SCALAR NORMAL 61 5.3.2 INVERTED GAMMA
OR SCALAR INVERTED WISHART 61 5.4 MULTIVARIATE NORMAL LIKELIHOOD 62
5.4.1 MULTIVARIATE NORMAL 62 5.4.2 INVERTED WISHART 62 5.5 MATRIX NORMAL
LIKELIHOOD 63 5.5.1 MATRIX NORMAL 63 5.5.2 INVERTED WISHART 64 6
BAYESIAN ESTIMATION METHODS 67 6.1 MARGINAL POSTERIOR MEAN 67 6.1.1
MATRIX INTEGRATION 68 6.1.2 GIBBS SAMPLING 70 6.1.3 GIBBS SAMPLING
CONVERGENCE 73 6.1.4 NORMAL VARIATE GENERATION 73 6.1.5 WISHART AND
INVERTED WISHART VARIATE GENERATION . . 74 6.1.6 FACTORIZATION 75 6.1.7
REJECTION SAMPLING 76 6.2 MAXIMUM A POSTERIORI 79 6.2.1 MATRIX
DIFFERENTIATION 80 6.2.2 ITERATED CONDITIONAL MODES (ICM) 80 6.3
ADVANTAGES OF ICM OVER GIBBS SAMPLING 82 6.4 ADVANTAGES OF GIBBS
SAMPLING OVER ICM 83 XLLL 7 REGRESSION 87 7.1 INTRODUCTION 87 7.2 NORMAL
SAMPLES 87 7.3 SIMPLE LINEAR REGRESSION 92 7.4 MULTIPLE LINEAR
REGRESSION 97 7.5 MULTIVARIATE LINEAR REGRESSION 98 II MODELS 111 8
BAYESIAN REGRESSION 113 8.1 INTRODUCTION 113 8.2 THE BAYESIAN REGRESSION
MODEL 113 8.3 LIKELIHOOD 115 8.4 CONJUGATE PRIORS AND POSTERIOR 116 8.5
CONJUGATE ESTIMATION AND INFERENCE 117 8.5.1 MARGINALIZATION 117 . 8.5.2
MAXIMUM A POSTERIORI 121 8.6 GENERALIZED PRIORS AND POSTERIOR 123 8.7
GENERALIZED ESTIMATION AND INFERENCE 124 8.7.1 MARGINALIZATION 124
8.7.2 POSTERIOR CONDITIONALS 127 8.7.3 GIBBS SAMPLING 127 8.7.4 MAXIMUM
A POSTERIORI 129 8.8 INTERPRETATION 131 8.9 DISCUSSION 134 9 BAYESIAN
FACTOR ANALYSIS 139 9.1 INTRODUCTION 139 9.2 THE BAYESIAN FACTOR
ANALYSIS MODEL 140 9.3 LIKELIHOOD 141 9.4 CONJUGATE PRIORS AND POSTERIOR
142 9.5 CONJUGATE ESTIMATION AND INFERENCE 144 9.5.1 POSTERIOR
CONDITIONALS 144 9.5.2 GIBBS SAMPLING 146 9.5.3 MAXIMUM A POSTERIORI 148
9.6 GENERALIZED PRIORS AND POSTERIOR 149 9.7 GENERALIZED ESTIMATION AND
INFERENCE 150 9.7.1 POSTERIOR CONDITIONALS 151 9.7.2 GIBBS SAMPLING 152,
9.7.3 MAXIMUM A POSTERIORI 154 9.8 INTERPRETATION 156 9.9 DISCUSSION 165
XIV 10 BAYESIAN SOURCE SEPARATION 169 10.1 INTRODUCTION 169 10.2 SOURCE
SEPARATION MODEL 169 10.3 SOURCE SEPARATION LIKELIHOOD 171 10.4
CONJUGATE PRIORS AND POSTERIOR 172 10.5 CONJUGATE ESTIMATION AND
INFERENCE 173 10.5.1 POSTERIOR CONDITIONALS 173 10.5.2 GIBBS SAMPLING
175 . 10.5.3 MAXIMUM A POSTERIORI 177 10.6 GENERALIZED PRIORS AND
POSTERIOR 179 10.7 GENERALIZED ESTIMATION AND INFERENCE 180 10.7.1
POSTERIOR CONDITIONALS 181 10.7.2 GIBBS SAMPLING 183 10.7.3 MAXIMUM A
POSTERIORI 185 10.8 INTERPRETATION 186 10.9 DISCUSSION 203 11
UNOBSERVABLE AND OBSERVABLE SOURCE SEPARATION 207 11.1 INTRODUCTION 207
11.2 MODEL 207 11.3 LIKELIHOOD 208 11.4 CONJUGATE PRIORS AND POSTERIOR
209 11.5 CONJUGATE ESTIMATION AND INFERENCE 211 11.5.1 POSTERIOR
CONDITIONALS 211 11.5.2 GIBBS SAMPLING 213 11.5.3 MAXIMUM A POSTERIORI
215 11.6 GENERALIZED PRIORS AND POSTERIOR 217 11.7 GENERALIZED
ESTIMATION AND INFERENCE 218 11.7.1 POSTERIOR CONDITIONALS 218 11.7.2
GIBBS SAMPLING 221 11.7.3 MAXIMUM A POSTERIORI 223 11.8 INTERPRETATION
224 11.9 DISCUSSION 225 12 FMRI CASE STUDY 229 12.1 INTRODUCTION 229
12.2 MODEL 230 12.3 PRIORS AND POSTERIOR 232 12.4 ESTIMATION AND
INFERENCE 233 12.5 SIMULATED FMRI EXPERIMENT 235 12.6 REAL FMRI
EXPERIMENT 246 12.7 FMRI CONCLUSION 248 III GENERALIZATIONS 251 13
DELAYED SOURCES AND DYNAMIC COEFFICIENTS 253 13.1 INTRODUCTION 253 13.2
MODEL 253 13.3 DELAYED CONSTANT MIXING 255 13.4 DELAYED NONCONSTANT
MIXING 257 13.5 INSTANTANEOUS NONCONSTANT MIXING 259 13.6 LIKELIHOOD 260
13.7 CONJUGATE PRIORS AND POSTERIOR 260 13.8 CONJUGATE ESTIMATION AND
INFERENCE 262 13.8.1 POSTERIOR CONDITIONALS 262 13.8.2 GIBBS SAMPLING
264 13.8.3 MAXIMUM A POSTERIORI 266 13.9 GENERALIZED PRIORS AND
POSTERIOR 268 13.10 GENERALIZED ESTIMATION AND INFERENCE 269 13.10.1
POSTERIOR CONDITIONALS 269 13.10.2 GIBBS SAMPLING 272 13.10.3 MAXIMUM A
POSTERIORI 273 13.11 INTERPRETATION 274 13.12 DISCUSSION 275 14
CORRELATED OBSERVATION AND SOURCE VECTORS 277 14.1 INTRODUCTION 277 14.2
MODEL 277 14.3 LIKELIHOOD 279 14.4 CONJUGATE PRIORS AND POSTERIOR , 281
14.5 CONJUGATE ESTIMATION AND INFERENCE 285 14.5.1 POSTERIOR
CONDITIONALS 285 14.5.2 GIBBS SAMPLING 290 14.5.3 MAXIMUM A POSTERIORI
293 14.6 GENERALIZED PRIORS AND POSTERIOR 295 14.7 GENERALIZED
ESTIMATION AND INFERENCE 297 14.7.1 POSTERIOR CONDITIONALS 297 14.7.2
GIBBS SAMPLING 300 14.7.3 MAXIMUM A POSTERIORI 302 14.8 INTERPRETATION
303 14.9 DISCUSSION 304 15 CONCLUSION 307 APPENDIX A FMRI ACTIVATION
DETERMINATION 309 A.I REGRESSION 309 A.2 GIBBS SAMPLING 312 A.3 ICM 313
APPENDIX B FMRI HYPERPARAMETER ASSESSMENT 315
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| spelling | Rowe, Daniel B. Verfasser aut Multivariate Bayesian statistics models for source separation and signal unmixing Daniel B. Rowe Boca Raton, FL Chapman & Hall/CRC 2003 XX, 329 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Análise multivariada larpcal Inferência bayesiana (análise de séries temporais) larpcal Methode van Bayes gtt Multivariate analyse gtt Teoria da decisão (inferência estatística) larpcal Bayesian statistical decision theory Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Bayes-Verfahren (DE-588)4204326-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009976544&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rowe, Daniel B. Multivariate Bayesian statistics models for source separation and signal unmixing Análise multivariada larpcal Inferência bayesiana (análise de séries temporais) larpcal Methode van Bayes gtt Multivariate analyse gtt Teoria da decisão (inferência estatística) larpcal Bayesian statistical decision theory Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4204326-8 |
| title | Multivariate Bayesian statistics models for source separation and signal unmixing |
| title_auth | Multivariate Bayesian statistics models for source separation and signal unmixing |
| title_exact_search | Multivariate Bayesian statistics models for source separation and signal unmixing |
| title_full | Multivariate Bayesian statistics models for source separation and signal unmixing Daniel B. Rowe |
| title_fullStr | Multivariate Bayesian statistics models for source separation and signal unmixing Daniel B. Rowe |
| title_full_unstemmed | Multivariate Bayesian statistics models for source separation and signal unmixing Daniel B. Rowe |
| title_short | Multivariate Bayesian statistics |
| title_sort | multivariate bayesian statistics models for source separation and signal unmixing |
| title_sub | models for source separation and signal unmixing |
| topic | Análise multivariada larpcal Inferência bayesiana (análise de séries temporais) larpcal Methode van Bayes gtt Multivariate analyse gtt Teoria da decisão (inferência estatística) larpcal Bayesian statistical decision theory Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Análise multivariada Inferência bayesiana (análise de séries temporais) Methode van Bayes Multivariate analyse Teoria da decisão (inferência estatística) Bayesian statistical decision theory Multivariate analysis Multivariate Analyse Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009976544&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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