Bayesian reasoning in data analysis: a critical introduction
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2003
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 329 S. Ill., graph. Darst. |
| ISBN: | 9812383565 |
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| adam_text | BAYESIAN REASONING IN DATA ANALYSIS A CRITICAL INTRODUCTION GIULIO
D AGOSTINI PHYSICS DEPARTMENT UNIVERSITY OF ROME LA SAPIENZA , ITALY
WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * HONG KONG CONTENTS
PART 1 CRITICAL REVIEW AND OUTLINE OF THE BAYESIAN ALTERNATIVE 1 1.
UNCERTAINTY IN PHYSICS AND THE USUAL METHODS OF HANDLING IT 3 1.1
UNCERTAINTY IN PHYSICS 3 1.2 TRUE VALUE, ERROR AND UNCERTAINTY 5 1.3
SOURCES OF MEASUREMENT UNCERTAINTY 6 1.4 USUAL HANDLING OF MEASUREMENT
UNCERTAINTIES 7 1.5 PROBABILITY OF OBSERVABLES VERSUS PROBABILITY OF
TRUE VALUES 9 1.6 PROBABILITY OF THE CAUSES . 11 1.7 UNSUITABILITY OF
FREQUENTISTIC CONFIDENCE INTERVALS . . . : . 11 1.8 MISUNDERSTANDINGS
CAUSED BY THE STANDARD PARADIGM OF HYPOTHESIS TESTS 15 1.9 STATISTICAL
SIGNIFICANCE VERSUS PROBABILITY OF HYPOTHESES . 19 2. A PROBABILISTIC
THEORY OF MEASUREMENT UNCERTAINTY 25 2.1 WHERE TO RESTART FROM? 25 2.2
CONCEPTS OF PROBABILITY 27 2.3 SUBJECTIVE PROBABILITY 29 2.4 LEARNING
FROM OBSERVATIONS: THE PROBLEM OF INDUCTION . 32 2.5 BEYOND POPPER S
FALSIFICATION SCHEME 34 XIV BAYESIAN REASONING IN DATA ANALYSIS: A
CRITICAL INTRODUCTION 2.6 FROM THE PROBABILITY OF THE EFFECTS TO THE
PROBABILITY OF THE CAUSES 34 2.7 BAYES THEOREM FOR UNCERTAIN QUANTITIES
36 2.8 AFRAID OF PREJUDICES ? LOGICAL NECESSITY VERSUS FREQUENT
PRACTICAL IRRELEVANCE OF PRIORS 37 2.9 RECOVERING STANDARD METHODS AND
SHORT-CUTS TO BAYESIAN REASONING 39 2.10 EVALUATION OF MEASUREMENT
UNCERTAINTY: GENERAL SCHEME . 41 2.10.1 DIRECT MEASUREMENT IN THE
ABSENCE OF SYSTEMATIC ERRORS 41 2.10.2 INDIRECT MEASUREMENTS 42 2.10.3
SYSTEMATIC ERRORS 43 2.10.4 APPROXIMATE METHODS 46 PART 2 A BAYESIAN
PRIMER 49 3. SUBJECTIVE PROBABILITY AND BAYES THEOREM 51 3.1 WHAT IS
PROBABILITY? 51 3.2 SUBJECTIVE DEFINITION OF PROBABILITY 52 3.3 RULES OF
PROBABILITY 55 3.4 SUBJECTIVE PROBABILITY AND OBJECTIVE DESCRIPTION OF
THE PHYSICAL WORLD 58 3.5 CONDITIONAL PROBABILITY AND BAYES THEOREM 60
3.5.1 DEPENDENCE OF THE PROBABILITY ON THE STATE OF INFORMATION 60 3.5.2
CONDITIONAL PROBABILITY . 61 3.5.3 BAYES THEOREM . 63 3.5.4
CONVENTIONAL USE OF BAYES THEOREM 66 3.6 BAYESIAN STATISTICS:
LEARNING BY EXPERIENCE 68 3.7 HYPOTHESIS TEST (DISCRETE CASE) 71 3.7.1
VARIATIONS OVER A PROBLEM TO NEWTON 72 3.8 FALSIFICATIONISM AND BAYESIAN
STATISTICS 76 3.9 PROBABILITY VERSUS DECISION 76 3.10 PROBABILITY OF
HYPOTHESES VERSUS PROBABILITY OF OBSERVATIONS 77 3.11 CHOICE OF THE
INITIAL PROBABILITIES (DISCRETE CASE) 78 3.11.1 GENERAL CRITERIA 78
3.11.2 INSUFFICIENT REASON AND MAXIMUM ENTROPY . . . . 81 CONTENTS XV
3.12 SOLUTION TO SOME PROBLEMS 82 3.12.1 AIDS TEST 82 3.12.2 GOLD/SILVER
RING PROBLEM 83 3.12.3 REGULAR OR DOUBLE-HEAD COIN? 84 3.12.4 WHICH
RANDOM GENERATOR IS RESPONSIBLE FOR THE OBSERVED NUMBER? 84 3.13 SOME
FURTHER EXAMPLES SHOWING THE CRUCIAL ROLE OF BACKGROUND KNOWLEDGE 85 4.
PROBABILITY DISTRIBUTIONS (A CONCISE REMINDER) 89 4.1 DISCRETE VARIABLES
89 4.2 CONTINUOUS VARIABLES: PROBABILITY AND PROBABILITY DENSITY
FUNCTION 92 4.3 DISTRIBUTION OF SEVERAL RANDOM VARIABLES 98 4.4
PROPAGATION OF UNCERTAINTY 104 4.5 CENTRAL LIMIT THEOREM 108 4.5.1 TERMS
AND ROLE 108 4.5.2 DISTRIBUTION OF A SAMPLE AVERAGE ILL 4.5.3 NORMAL
APPROXIMATION OF THE BINOMIAL AND OF THE POISSON DISTRIBUTION ILL 4.5.4
NORMAL DISTRIBUTION OF MEASUREMENT ERRORS . . . 112 4.5.5 CAUTION 112
4.6 LAWS OF LARGE NUMBERS 113 5. BAYESIAN INFERENCE OF CONTINUOUS
QUANTITIES 115 5.1 MEASUREMENT ERROR AND MEASUREMENT UNCERTAINTY . ... .
115 5.1.1 GENERAL FORM OF BAYESIAN INFERENCE . 116 5.2 BAYESIAN
INFERENCE AND MAXIMUM LIKELIHOOD 118 5.3 THE DOG, THE HUNTER AND THE
BIASED BAYESIAN ESTIMATORS . 119 5.4 CHOICE OF THE INITIAL PROBABILITY
DENSITY FUNCTION 120 5.4.1 DIFFERENCE WITH RESPECT TO THE DISCRETE CASE
. . . 120 5.4.2 BERTRAND PARADOX AND ANGELS SEX 121 6. GAUSSIAN
LIKELIHOOD 123 6.1 NORMALLY DISTRIBUTED OBSERVABLES 123 6.2 FINAL
DISTRIBUTION, PREVISION AND CREDIBILITY INTERVALS OF THE TRUE VALUE 124
6.3 COMBINATION OF SEVERAL MEASUREMENTS - ROLE OF PRIORS . . 125 XVI
BAYESIAN REASONING IN DATA ANALYSIS: A CRITICAL INTRODUCTION 6.3.1
UPDATE OF ESTIMATES IN TERMS OF KALMAN FILTER . . 126 6.4 CONJUGATE
PRIORS 126 6.5 IMPROPER PRIORS * NEVER TAKE MODELS LITERALLY! 127 6.6
PREDICTIVE DISTRIBUTION 127 6.7 MEASUREMENTS CLOSE TO THE EDGE OF THE
PHYSICAL REGION . . 128 6.8 UNCERTAINTY OF THE INSTRUMENT SCALE OFFSET
131 6.9 CORRECTION FOR KNOWN SYSTEMATIC ERRORS 133 6.10 MEASURING TWO
QUANTITIES WITH THE SAME INSTRUMENT HAVING AN UNCERTAINTY OF THE SCALE
OFFSET 133 6.11 INDIRECT CALIBRATION 136 6.12 THE GAUSS DERIVATION OF
THE GAUSSIAN 137 7. COUNTING EXPERIMENTS 141 7.1 BINOMIALLY DISTRIBUTED
OBSERVABLES 141 7.1.1 OBSERVING 0% OR 100% 145 7.1.2 COMBINATION OF
INDEPENDENT MEASUREMENTS . . . 146 7.1.3 CONJUGATE PRIOR AND MANY DATA
LIMIT 146 7.2 THE BAYES PROBLEM 148 7.3 PREDICTING RELATIVE FREQUENCIES
- TERMS AND INTERPRETATION OF BERNOULLI S THEOREM 148 7.4 POISSON
DISTRIBUTED OBSERVABLES 152 7.4.1 OBSERVATION OF ZERO COUNTS 154 7.5
CONJUGATE PRIOR OF THE POISSON LIKELIHOOD 155 7.6 PREDICTING FUTURE
COUNTS 155 7.7 A DEEPER LOOK TO THE POISSONIAN CASE 156 7.7.1 DEPENDENCE
ON PRIORS * PRACTICAL EXAMPLES . **.. . 156 7.7.2 COMBINATION OF RESULTS
FROM SIMILAR EXPERIMENTS 158 7.7.3 COMBINATION OF RESULTS: GENERAL CASE
160 7.7.4 INCLUDING SYSTEMATIC EFFECTS 162 7.7.5 COUNTING MEASUREMENTS
IN THE PRESENCE OF BACKGROUND 165 8. BYPASSING BAYES THEOREM FOR
ROUTINE APPLICATIONS 169 8.1 MAXIMUM LIKELIHOOD AND LEAST SQUARES AS
PARTICULAR CASES OF BAYESIAN INFERENCE 169 8.2 LINEAR FIT 172 8.3 LINEAR
FIT WITH ERRORS ON BOTH AXES 175 8.4 MORE COMPLEX CASES 176 CONTENTS
XVII 8.5 SYSTEMATIC ERRORS AND INTEGRATED LIKELIHOOD 177 8.6
LINEARIZATION OF THE EFFECTS OF INFLUENCE QUANTITIES AND APPROXIMATE
FORMULAE 178 8.7 BIPM AND ISO RECOMMENDATIONS 181 8.8 EVALUATION OF TYPE
B UNCERTAINTIES 183 8.9 EXAMPLES OF TYPE B UNCERTAINTIES 184 8.10
COMMENTS ON THE USE OF TYPE B UNCERTAINTIES 186 8.11 CAVEAT CONCERNING
THE BLIND USE OF APPROXIMATE METHODS 189 8.12 PROPAGATION OF UNCERTAINTY
191 8.13 COVARIANCE MATRIX OF EXPERIMENTAL RESULTS - MORE DETAILS 192
8.13.1 BUILDING THE COVARIANCE MATRIX OF EXPERIMENTAL DATA 192 8.13.1.1
OFFSET UNCERTAINTY 193 8.13.1.2 NORMALIZATION UNCERTAINTY 195 8.13.1.3
GENERAL CASE 196 8.14 USE AND MISUSE OF THE COVARIANCE MATRIX TO FIT
CORRELATED DATA 197 8.14.1 BEST ESTIMATE OF THE TRUE VALUE FROM TWO
CORRELATED VALUES 197 8.14.2 OFFSET UNCERTAINTY 198 8.14.3 NORMALIZATION
UNCERTAINTY 198 8.14.4 PEELLE S PERTINENT PUZZLE 202 9. BAYESIAN
UNFOLDING 203 9.1 PROBLEM AND TYPICAL SOLUTIONS 203 9.2 BAYES THEOREM
STATED IN TERMS OF CAUSES AND EFFECTS . . . 204 9.3 UNFOLDING AN
EXPERIMENTAL DISTRIBUTION 205 PART 3 FURTHER COMMENTS, EXAMPLES AND
APPLICA- TIONS 209 10. MISCELLANEA ON GENERAL ISSUES IN PROBABILITY AND
INFERENCE 211 10.1 UNIFYING ROLE OF SUBJECTIVE APPROACH 211 10.2
FREQUENTISTS AND COMBINATORIAL EVALUATION OF PROBABILITY . 213 10.3
INTERPRETATION OF CONDITIONAL PROBABILITY 215 10.4 ARE THE BELIEFS IN
CONTRADICTION TO THE PERCEIVED OBJECTIVITY OF PHYSICS? 216 10.5
FREQUENTISTS AND BAYESIAN SECTS 220 XVIII BAYESIAN REASONING IN DATA
ANALYSIS: A CRITICAL INTRODUCTION 10.5.1 BAYESIAN VERSUS FREQUENTISTIC
METHODS 221 10.5.2 SUBJECTIVE OR OBJECTIVE BAYESIAN THEORY? .... 222
10.5.3 BAYES THEOREM IS NOT EVERYTHING 226 10.6 BIASED BAYESIAN
ESTIMATORS AND MONTE CARLO CHECKS OF BAYESIAN PROCEDURES 226 10.7
FREQUENTISTIC COVERAGE 229 10.7.1 ORTHODOX TEACHER VERSUS SHARP STUDENT
- A DIALOGUE BY GEORGE GABOR 232 10.8 WHY DO FREQUENTISTIC HYPOTHESIS
TESTS OFTEN WORK ? . . . 233 10.9 COMPARING COMPLEX HYPOTHESES -
AUTOMATIC OCKHAM RAZOR 239 10.10 BAYESIAN NETWORKS 241 10.10.1 NETWORKS
OF BELIEFS - CONCEPTUAL AND PRACTICAL APPLICATIONS 241 10.10.2 THE
GOLD/SILVER RING PROBLEM IN TERMS OF BAYESIAN NETWORKS 242 11.
COMBINATION OF EXPERIMENTAL RESULTS: A CLOSER LOOK 247 11.1 USE AND
MISUSE OF THE STANDARD COMBINATION RULE 247 11.2 APPARENTLY
INCOMPATIBLE EXPERIMENTAL RESULTS 249 11.3 SCEPTICAL COMBINATION OF
EXPERIMENTAL RESULTS 252 11.3.1 APPLICATION TO E /E 259 11.3.2 POSTERIOR
EVALUATION OF (JJ 262 12. ASYMMETRIC UNCERTAINTIES AND NONLINEAR
PROPAGATION 267 12.1 USUAL COMBINATION OF STATISTIC AND SYSTEMATIC
ERRORS . . 267 12.2 SOURCES OF ASYMMETRIC UNCERTAINTIES IN STANDARD
STATISTICAL PROCEDURES 269 12.2.1 ASYMMETRIC X 2 AND AX 2 = 1 RULE 269
12.2.2 SYSTEMATIC EFFECTS 272 12.2.2.1 ASYMMETRIC BELIEFS ON SYSTEMATIC
EFFECTS 273 12.2.2.2 NONLINEAR PROPAGATION OF UNCERTAINTIES 273 12.3
GENERAL SOLUTION OF THE PROBLEM 273 12.4 APPROXIMATE SOLUTION 275 12.4.1
LINEAR EXPANSION AROUND E(X) 276 12.4.2 SMALL DEVIATIONS FROM LINEARITY
278 CONTENTS XIX 12.5 NUMERICAL EXAMPLES 280 12.6 THE NON-MONOTONIC CASE
282 13. WHICH PRIORS FOR FRONTIER PHYSICS? 285 13.1 FRONTIER PHYSICS
MEASUREMENTS AT THE LIMIT TO THE DETECTOR SENSITIVITY 285 13.2
DESIDERATA FOR AN OPTIMAL REPORT OF SEARCH RESULTS . . . . 286 13.3
MASTER EXAMPLE: INFERRING THE INTENSITY OF A POISSON PROCESS IN THE
PRESENCE OF BACKGROUND 287 13.4 MODELLING THE INFERENTIAL PROCESS 288
13.5 CHOICE OF PRIORS 288 13.5.1 UNIFORM PRIOR 289 13.5.2 JEFFREYS
PRIOR 290 13.5.3 ROLE OF PRIORS 292 13.5.4 PRIORS REFLECTING THE
POSITIVE ATTITUDE OF RESEARCHERS 292 13.6 PRIOR-FREE PRESENTATION OF THE
EXPERIMENTAL EVIDENCE . . . 295 13.7 SOME EXAMPLES OF 7-FUNCTION BASED
ON REAL DATA 298 13.8 SENSITIVITY BOUND VERSUS PROBABILISTIC BOUND 299
13.9 OPEN VERSUS CLOSED LIKELIHOOD 302 PART 4 CONCLUSION 305 14.
CONCLUSIONS AND BIBLIOGRAPHY 307 14.1 ABOUT SUBJECTIVE PROBABILITY AND
BAYESIAN INFERENCE . . . 307 14.2 CONSERVATIVE OR REALISTIC UNCERTAINTY
EVALUATION? ...... 308 14.3 ASSESSMENT OF UNCERTAINTY IS NOT A
MATHEMATICAL GAME . 310 14.4 BIBLIOGRAPHIC NOTE 310 BIBLIOGRAPHY 313
INDEX 325
|
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| isbn | 9812383565 |
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| spelling | D'Agostini, Giulio Verfasser aut Bayesian reasoning in data analysis a critical introduction Giulio D'Agostini New Jersey [u.a.] World Scientific 2003 XIX, 329 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Datenanalyse (DE-588)4123037-1 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=013071701&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | D'Agostini, Giulio Bayesian reasoning in data analysis a critical introduction Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4123037-1 |
| title | Bayesian reasoning in data analysis a critical introduction |
| title_auth | Bayesian reasoning in data analysis a critical introduction |
| title_exact_search | Bayesian reasoning in data analysis a critical introduction |
| title_full | Bayesian reasoning in data analysis a critical introduction Giulio D'Agostini |
| title_fullStr | Bayesian reasoning in data analysis a critical introduction Giulio D'Agostini |
| title_full_unstemmed | Bayesian reasoning in data analysis a critical introduction Giulio D'Agostini |
| title_short | Bayesian reasoning in data analysis |
| title_sort | bayesian reasoning in data analysis a critical introduction |
| title_sub | a critical introduction |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Bayes-Verfahren Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013071701&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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