Pragmatics of Uncertainty (Chapman & Hall/CRC Texts in Statistical Science)

A fair question to ask of an advocate of subjective Bayesianism (which the author is) is "how would you model uncertainty?" In this book, the author writes about how he has done it using real problems from the past, and offers additional comments about the context in which he was working.-- Provided by Publisher Cover 1 Half Title 2 Title Page 6 Copyright Page 7 Dedication 8 Table of Contents 10 Foreword 16 Preface 18 1: Bayesian Paleoethnobotany (1988) 20 Foreword 20 Published Paper 22 1.1 Styles of Data Analysis 22 1.2 The Data 22 1.3 Research Plan 25 1.4 Prior Probabilities of Activities 27 1.5 Botanical Remains: The Likelihood Function 32 1.6 Computation of Posterior Distributions 34 1.7 Conclusion 36 References 41 Discussion 42 Reply to the Discussion 43 Epilogue 44 Teaching Suggestions 45 2: Statistical Sampling in Tax Audits (1988) 46 Foreword 46 Published Paper 48 2.1 Introduction 48 2.2 The Theory of Statistical Sampling: An Overview 49 2.3 Judicial Decisions 51 2.4 The Case for Statistical Samples 58 2.5 Statutory Standards for the Use of Statistical Sampling 60 2.6 Conclusions 68 Appendix A 68 Epilogue 69 Teaching Suggestions 70 3: A Statistical Analysis of Adverse Impact of Employer Decisions (1990) 72 Foreword 72 Published Paper 74 3.1 Introduction 74 3.2 Database Issues 75 3.3 Analyses 76 3.3.1 Fisher's Exact Tests 77 3.3.2 A Bayesian Analysis 79 3.3.3 Paired Observations 85 3.4 Conclusions 87 References 87 Epilogue 88 Teaching Suggestions 89 4: Subjective Bayesian Analysis for Surveys with Missing Data (1993) 90 Foreword 90 Published Paper 92 4.1 Introduction 92 4.2 Background and Analysis 93 4.3 Conclusions 101 References 103 Epilogue 105 Teaching Suggestions 105 5: Missing Data in the Forensic Context (1997) 108 Foreword 108 Published Paper 110 5.1 Introduction 110 5.2 The New Jersey Turnpike Case 110 5.3 Presentation to Court of Surveys with Missing Data 114 References 115 Epilogue 116 Teaching Suggestions 116 6: Bayesian Demography: Projecting the Iraqi Kurdish Population, 1977–1990 (1997) 118 Foreword 118 Published Paper 120 6.1 Introduction 120 6.2 Current Practices 122 6.3 The Iraqi Kurdish Population 125 6.4 Overview of Projection Procedure 127 6.5 Projecting the Iraqi Kurdish Population 127 6.5.1 Fertility 127 6.5.2 Mortality 130 6.5.3 Migration 133 6.5.4 Obtaining a Base Population 133 6.6 Results 135 6.7 Discussion 139 References 139 Epilogue 141 Teaching Suggestions 142 7: An Allegation of Examination Copying (1999) 144 Foreword 144 Published Paper 146 7.1 Data and Formal Analysis 146 7.2 Priors: What to Look For 147 7.3 An Index 147 7.4 Results 148 7.5 Conclusion 151 7.6 Other Purposes, Other Indices 152 References 153 Epilogue 153 Teaching Suggestions 153 8: Vote Tampering in a District Justice Election in Beaver County, PA (2001) 156 Foreword 156 Published Paper 158 8.1 Introduction 158 8.2 Legal History 160 8.3 Model 161 8.3.1 Data Structuring 162 8.3.2 Model Specification 162 8.3.3 Estimation with Markov Chain Monte Carlo 166 8.4 Results 167 8.4.1 Model Validation 169 8.5 Discussion 170 Appendix 171 References 173 Epilogue 173 Teaching Suggestions 174 9: The Effect of Intensity of Effort to Reach Survey Respondents: A Toronto Smoking Survey (2001) 176 Foreword 176 Published Paper 178 9.1 Introduction 178 9.2 The Survey 179 9.3 Overview of Methodology 180 9.4 MAR Models 181 9.4.1 Logistic Regression 181 9.4.2 Bayesian Logistic Regression 182 9.5 NI Model 182 9.5.1 Modeling the Non-Response Mechanism 182 9.5.2 Relating Non-Response to the Dependent Variable - The NI Model 185 9.5.3 Data Augmentation 186 9.5.4 Sampling from the Posterior Distribution 187 9.6 Choice of Prior Distributions 188 9.7 Results 189 9.7.1 Coefficients for the Number of Calls 189 9.7.2 Sensitivity to Priors 189 9.7.3 Effect on Odds of Response 190 9.7.4 Effect on Probability of Response 192 9.8 Conclusion 192 Appendices 193 References 194 Epilogue 195 Teaching Suggestions 196 10: Comparing Harm Done by Mobility and Class Absence: Missing Students and Missing Data (2003) 198 Foreword 198 Published Paper 200 10.1 Introduction 200 10.2 Data 201 10.2.1 Data Description 201 10.2.2 Missing Data 203 10.3 Model Specifcation 204 10.3.1 Notation 204 10.3.2 Likelihood without Choice Indicators 204 10.3.3 Likelihood with Choice Indicators 206 10.3.4 Prior Distributions 207 10.4 Methodology for Sampling from the Posterior Distribution 208 10.5 Results 208 10.6 Conclusions 211 10.7 Discussion 213 Appendix 213 References 215 Editor's Foreword 216 Comment 217 Epilogue 218 Teaching Suggestions 219 11: Hierarchical Models for Employment Decisions (2004) 220 Foreword 220 Published Paper 222 11.1 Introduction 222 11.2 Proportional Hazards Models 224 11.2.1 Hierarchical Priors for Time Varying Coefficients 226 11.2.2 Smoothness Priors 227 11.2.3 Forming an Opinion about Smoothness 227 11.2.4 Posterior Distribution 228 11.2.5 Reexpressing β 229 11.3 Examples 230 11.3.1 Case K 230 11.3.2 Case W 236 11.3.3 Valentino v. United States Postal Service 240 11.4 Discussion 241 References 243 Epilogue 244 Teaching Suggestions 244 12: Age- and Time-Varying Proportional Hazards Models for Employment Discrimination (2010) 246 Foreword 246 Published Paper 248 12.1 Introduction 248 12.2 Proportional Hazards Regression 249 12.2.1 Overview 250 12.2.2 Proportional Hazards Models for Time to Event Data 250 12.2.3 Thin-Plate Spline Smoothness Priors 252 12.3 Case W Revisited 254 12.3.1 Forming an Opinion about Smoothness and Anisotropy 255 12.3.2 Computing the Posterior Distribution 256 12.3.3 Sensitivity Analysis 257 12.3.4 Identifcation of the Anisotropy Parameter 258 12.3.5 Previous Analyses of Case W 259 12.3.6 Summary 261 12.4 Discussion 262 References 263 Epilogue 264 Teaching Suggestions 264 13: Error Analysis for Small Angle Neutron Scattering Datasets Using Bayesian Inference (2010) 266 Foreword 266 Published Paper 268 13.1 Introduction 268 13.1.1 Correlation Lengths 271 13.1.2 Small-angle Neutron Scattering 273 13.2 The SANS Instrument 274 13.2.1 Instrument Components 274 13.2.2 Instrument Configurations 276 13.3 SANS Error Analysis 277 13.3.1 Traditional Error Analysis 277 13.3.2 The Bayesian Alternative 278 13.4 Results and Discussion 285 13.4.1 Separate Marginal Distributions on ξL and ξS 287 13.4.2 Joint Posterior Distribution on (ξL, ξS) 287 13.4.3 Representing Fits Graphically: "family of curves" and Standardized Residual Distributions 289 13.5 Conclusions 290 Appendix A 291 Appendix B 292 References 293 Comment 294 Comment 296 Rejoinder 297 Epilogue 299 Teaching Suggestions 299 14: Impacts of Beliefs about Tropical Cyclone Detection on Conclusions about Trends in Tropical Cyclone Number (2011) 302 Foreword 302 Published Paper 304 14.1 Introduction 304 14.2 TC Detection and Recording over the Years 306 14.3 Combining Detection Probability with Raw Counts 308 14.4 Illustration 310 14.5 Sensitivity to Prior Quantification 312 14.6 Concluding Remarks 316 14.6.1 Resolving Ambiguity with Further Studies 316 14.6.2 Sensitivity to Formulation 316 14.6.3 Toward a Flexible Formulation 317 14.6.4 Incorporating Climate Models 317 References 318 Epilogue 321 Teaching Suggestions 322 15: The Number of Killings in Southern Rural Norway, 1300-1569 (2013) 324 Foreword 324 Published Paper 326 15.1 Norwegian Homicide Law and the Documentary Evidence 326 15.2 Demographic Evidence about the Number of Killings 327 15.3 Models of the Data 328 15.4 Conclusion 336 References 337 Epilogue 337 Teaching Suggestions 338 Epilogue 340 Index 342 Index of Names 348 Content: 1. Bayesian paleoethnobotany (1988) -- 2. Statistical sampling in tax audits (1988) -- 3. A statistical analysis of adverse impact of employer decisions (1990) -- 4. Subjective Bayesian analysis for surveys with missing data (1993) -- 5. Missing data in the forensic context (1997) -- 6. Bayesian demography : projecting the Iraqi Kurdish population, 1997-1990 (1997) -- 7. An allegation of examination copying (1999) -- 8. Vote tampering in a district justice election in Beaver County, PA (2001) -- 9. The effect of intensity of effort to reach survey respondents : a Toronto smoking survey (2001) -- 10. Comparing harm done by mobility and class absence : missing students and missing data (2003) -- 11. Hierarchical models for employment decisions (2004) -- 12. Age- and time- varying proportional hazards models for employment discrimination (2010) -- 13. Error analysis for small angle neutron scattering datasets using Bayesian inference (2010) -- 14. Impacts of beliefs about tropical cyclone detection on conclusions about trends in tropical cyclone number (2011) -- 15. The number of killings in southern rural Norway, 1300-1569 (2013).