Robustness of Bayesian analysis:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1984
|
| Series: | Studies in Bayesian econometrics
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 314 S. |
| ISBN: | 0444862099 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
Introduction to the series v
Preface vii
PART I: BAYESIAN STATISTICAL INFERENCE FOR
PSYCHOLOGICAL RESEARCH 1
Ward Edwards, Harold Lindman and Leonard J. Savage
1. Introduction 2
2. Elements of Bayesian statistics 4
3. Principle of stable estimation 10
4. A smattering of Bayesian distribution theory 20
5. Point and interval estimation 25
6. Introduction to hypothesis testing 26
7. Bayesian hypothesis testing 30
8. Likelihood principle 56
9. In retrospect 59
References 60
PART II: THE ROBUST BAYESIAN VIEWPOINT 63
James O. Berger
1. Introduction 64
1.1. Introduction 64
1.2. Notation 66
1.3. Decision theory 66
2. The robust Bayesian viewpoint 68
2.1. Justification for Assumption I 68
2.2. Justification for Assumption II 71
2.3. Reasonable classes of prior distributions 73
2.4. Updating T 75
3. Measures of robustness 78
3.1. Posterior robustness 78
ix
x Contents
3.2. Procedure robustness 79
3.3. Discussion 81
4. Implications of the robust Bayesian viewpoint 83
4.1. Data analysis 83
4.2. Randomization 83
4.3. Classical robustness 85
4.4. Uses of frequency measures 85
4.5. Estimating a multivariate mean: The Stein effect 88
5. History and guidelines 92
5.1. History 92
5.2. Guidelines 101
6. Final comments 106
6.1. Non Bayesian criticisms 106
6.2. Bayesian criticisms 107
6.3. Foundational criticisms 109
6.4. Future development 113
Acknowledgements 114
References 115
PART III: COMMENTS ON THE ROBUST BAYESIAN
VIEWPOINT BY JAMES BERGER 125
1. Comment by Lawrence D. Brown 126
2. Comment by Bruce M. Hill 134
3. Comment by Joseph B. Kadane 136
4. Comment by Dennis V. Lindley 137
5. Reply by James O. Berger 139
PART IV: STABLE DECISION PROBLEMS 145
Joseph B. Kadane and David T. Chuang
1. Introduction 146
2. A general structure theorem and some examples 149
3. Bounded continuous loss functions 154
4. Estimation or prediction loss functions with bounded growth 156
5. Conclusion 162
References 163
Contents xi
PART V: FURTHER THEORY OF STABLE DECISIONS 165
David T. Chuang
1. Introduction 166
1.1. Formulation of the problem 166
1.2. Explanation of definitions 171
1.3. Outline of paper 172
2. A general structure and convergence of Pn(8) 174
2.1. A general structure and new definitions 174
2.2. Convergence of Pn{0) 179
3. Relationships among Definitions I, II, III and IV 181
3.1. Relationships for general loss function 181
3.2. Relationships of definitions in estimation or prediction problem 185
4. Necessary and sufficient conditions for stability in the estimation or
prediction case 200
4.1. When loss of function is uniformly bounded or uniformly bounded
on one side and unbounded on the other side 200
4.2. The case Yaax^±Ji{x) = +°° 203
5. Stable decision problems related to l(x | 0) = 1 216
5.1. Review 216
5.2. Stability, independent of opinion 218
5.3. Necessary and sufficient conditions for stability 222
5.4. Examples 223
5.5. Some relations between the two sets of definitions 225
6. Conclusions and topics for further research 227
References 228
PART VI: MULTIVARIATE REGRESSION SYSTEMS
ESTIMATION AND SENSITIVITY ANALYSIS OF
TWO DIMENSIONAL DATA 229
Wolfgang Polasek
Preface 230
1. Introduction 231
Section I: Econometric Theory for One and Two Dimensional Data 234
xii Contents
2. Estimation and sensitivity analysis in one dimensional models 234
2.1. The information contract curve 234
2.2. Ellipsoids and the linear model 235
2.3. Prior variance bounds in a Bayesian analysis 240
Appendix 2.A: Inversion lemmas 245
3. Hierarchical regression models 246
3.1. Introduction 246
3.2. Informative hierarchical models 246
3.3. Noninformative hierarchical models 249
Appendix 3.A: Proof of Theorem 3.3.1 251
Section II: Applications: Selected Models for Two Dimensional Data 252
4. A hierarchical analysis of the investment function 252
4.1. Introduction 252
4.2. Hierarchical bound analysis 252
4.3. A hierarchical bound analysis of the Griinfeld investment
function 255
Appendix 4.A: Modal estimate of the posterior distribution 259
5. Hierarchical load curve models 261
5.1. Introduction 261
5.2. The three stage load curve model 261
5.3. Bayes estimates for a quadratic hierarchical load curve model 266
5.4. Sensitivity analysis for a 16 household example 269
6. The hierarchical coefficient load curve model 278
6.1. Introduction 278
6.2. The coefficient load curve approach 278
6.3. The three stage coefficient load curve model 281
6.4. Application to residential electricity demand 283
7. Hierarchical seasonal distributed lag model 292
7.1. Introduction 292
7.2. Seasonal distributed lag (SDL) models 292
7.3. Noninformative hierarchical SDL models 294
7.4. The informative hierarchical SDL model 297
7.5. The hierarchical seasonal ridge type model 300
7.6. The informative seasonal smoothness model 303
Outlook and open problems 305
References 307
Index 311
|
| adam_txt |
CONTENTS
Introduction to the series v
Preface vii
PART I: BAYESIAN STATISTICAL INFERENCE FOR
PSYCHOLOGICAL RESEARCH 1
Ward Edwards, Harold Lindman and Leonard J. Savage
1. Introduction 2
2. Elements of Bayesian statistics 4
3. Principle of stable estimation 10
4. A smattering of Bayesian distribution theory 20
5. Point and interval estimation 25
6. Introduction to hypothesis testing 26
7. Bayesian hypothesis testing 30
8. Likelihood principle 56
9. In retrospect 59
References 60
PART II: THE ROBUST BAYESIAN VIEWPOINT 63
James O. Berger
1. Introduction 64
1.1. Introduction 64
1.2. Notation 66
1.3. Decision theory 66
2. The robust Bayesian viewpoint 68
2.1. Justification for Assumption I 68
2.2. Justification for Assumption II 71
2.3. Reasonable classes of prior distributions 73
2.4. Updating T 75
3. Measures of robustness 78
3.1. Posterior robustness 78
ix
x Contents
3.2. Procedure robustness 79
3.3. Discussion 81
4. Implications of the robust Bayesian viewpoint 83
4.1. Data analysis 83
4.2. Randomization 83
4.3. Classical robustness 85
4.4. Uses of frequency measures 85
4.5. Estimating a multivariate mean: The Stein effect 88
5. History and guidelines 92
5.1. History 92
5.2. Guidelines 101
6. Final comments 106
6.1. Non Bayesian criticisms 106
6.2. Bayesian criticisms 107
6.3. Foundational criticisms 109
6.4. Future development 113
Acknowledgements 114
References 115
PART III: COMMENTS ON "THE ROBUST BAYESIAN
VIEWPOINT" BY JAMES BERGER 125
1. Comment by Lawrence D. Brown 126
2. Comment by Bruce M. Hill 134
3. Comment by Joseph B. Kadane 136
4. Comment by Dennis V. Lindley 137
5. Reply by James O. Berger 139
PART IV: STABLE DECISION PROBLEMS 145
Joseph B. Kadane and David T. Chuang
1. Introduction 146
2. A general structure theorem and some examples 149
3. Bounded continuous loss functions 154
4. Estimation or prediction loss functions with bounded growth 156
5. Conclusion 162
References 163
Contents xi
PART V: FURTHER THEORY OF STABLE DECISIONS 165
David T. Chuang
1. Introduction 166
1.1. Formulation of the problem 166
1.2. Explanation of definitions 171
1.3. Outline of paper 172
2. A general structure and convergence of Pn(8) 174
2.1. A general structure and new definitions 174
2.2. Convergence of Pn{0) 179
3. Relationships among Definitions I, II, III and IV 181
3.1. Relationships for general loss function 181
3.2. Relationships of definitions in estimation or prediction problem 185
4. Necessary and sufficient conditions for stability in the estimation or
prediction case 200
4.1. When loss of function is uniformly bounded or uniformly bounded
on one side and unbounded on the other side 200
4.2. The case Yaax^±Ji{x) = +°° 203
5. Stable decision problems related to l(x | 0) = 1 216
5.1. Review 216
5.2. Stability, independent of opinion 218
5.3. Necessary and sufficient conditions for stability 222
5.4. Examples 223
5.5. Some relations between the two sets of definitions 225
6. Conclusions and topics for further research 227
References 228
PART VI: MULTIVARIATE REGRESSION SYSTEMS
ESTIMATION AND SENSITIVITY ANALYSIS OF
TWO DIMENSIONAL DATA 229
Wolfgang Polasek
Preface 230
1. Introduction 231
Section I: Econometric Theory for One and Two Dimensional Data 234
xii Contents
2. Estimation and sensitivity analysis in one dimensional models 234
2.1. The information contract curve 234
2.2. Ellipsoids and the linear model 235
2.3. Prior variance bounds in a Bayesian analysis 240
Appendix 2.A: Inversion lemmas 245
3. Hierarchical regression models 246
3.1. Introduction 246
3.2. Informative hierarchical models 246
3.3. Noninformative hierarchical models 249
Appendix 3.A: Proof of Theorem 3.3.1 251
Section II: Applications: Selected Models for Two Dimensional Data 252
4. A hierarchical analysis of the investment function 252
4.1. Introduction 252
4.2. Hierarchical bound analysis 252
4.3. A hierarchical bound analysis of the Griinfeld investment
function 255
Appendix 4.A: Modal estimate of the posterior distribution 259
5. Hierarchical load curve models 261
5.1. Introduction 261
5.2. The three stage load curve model 261
5.3. Bayes estimates for a quadratic hierarchical load curve model 266
5.4. Sensitivity analysis for a 16 household example 269
6. The hierarchical coefficient load curve model 278
6.1. Introduction 278
6.2. The coefficient load curve approach 278
6.3. The three stage coefficient load curve model 281
6.4. Application to residential electricity demand 283
7. Hierarchical seasonal distributed lag model 292
7.1. Introduction 292
7.2. Seasonal distributed lag (SDL) models 292
7.3. Noninformative hierarchical SDL models 294
7.4. The informative hierarchical SDL model 297
7.5. The hierarchical seasonal ridge type model 300
7.6. The informative seasonal smoothness model 303
Outlook and open problems 305
References 307
Index 311 |
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| index_date | 2024-07-02T16:16:26Z |
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| institution | BVB |
| isbn | 0444862099 |
| language | English |
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| physical | 314 S. |
| publishDate | 1984 |
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| publisher | North-Holland |
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| series | Studies in Bayesian econometrics |
| series2 | Studies in Bayesian econometrics |
| spelling | Robustness of Bayesian analysis ed. by Joseph B. Kadane Amsterdam [u.a.] North-Holland 1984 314 S. txt rdacontent n rdamedia nc rdacarrier Studies in Bayesian econometrics 4 Analyse statistique Décision Methode van Bayes gtt Modèle statistique Régression Bayesian statistical decision theory Robust statistics Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s DE-604 Robuste Statistik (DE-588)4451047-0 s Kadane, Joseph B. Sonstige oth Studies in Bayesian econometrics 4 (DE-604)BV000011425 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015339673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robustness of Bayesian analysis Studies in Bayesian econometrics Analyse statistique Décision Methode van Bayes gtt Modèle statistique Régression Bayesian statistical decision theory Robust statistics Bayes-Verfahren (DE-588)4204326-8 gnd Robuste Statistik (DE-588)4451047-0 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4451047-0 |
| title | Robustness of Bayesian analysis |
| title_auth | Robustness of Bayesian analysis |
| title_exact_search | Robustness of Bayesian analysis |
| title_exact_search_txtP | Robustness of Bayesian analysis |
| title_full | Robustness of Bayesian analysis ed. by Joseph B. Kadane |
| title_fullStr | Robustness of Bayesian analysis ed. by Joseph B. Kadane |
| title_full_unstemmed | Robustness of Bayesian analysis ed. by Joseph B. Kadane |
| title_short | Robustness of Bayesian analysis |
| title_sort | robustness of bayesian analysis |
| topic | Analyse statistique Décision Methode van Bayes gtt Modèle statistique Régression Bayesian statistical decision theory Robust statistics Bayes-Verfahren (DE-588)4204326-8 gnd Robuste Statistik (DE-588)4451047-0 gnd |
| topic_facet | Analyse statistique Décision Methode van Bayes Modèle statistique Régression Bayesian statistical decision theory Robust statistics Bayes-Verfahren Robuste Statistik |
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