Weight-of-Evidence for Forensic DNA Profiles

Editors:D. J. Balding, Imperial College of Science, Technology and Medicine, London, UK M. Bishop, UK HGMP Resource Centre, Cambridge, UK C. Cannings, University of Sheffield, UK

• Preface xi1 Introduction 11.1 Weight-of-evidence theory 11.2 About the book 31.3 DNA profiling technology 31.4 What you need to know already 41.5 Other resources 52 Crime on an island 72.1 Warm-up examples 72.1.1 Disease testing: Positive Predictive Value (PPV) 72.1.2 Coloured taxis 92.2 Rare trait identification evidence 102.2.1 The “island” problem 102.2.2 A first lesson from the island problem 112.3 Making the island problem more realistic 132.3.1 Uncertainty about p 142.3.2 Uncertainty about N 152.3.3 Possible typing errors 152.3.4 Searches 172.3.5 Other evidence 182.3.6 Relatives and population subdivision 192.4 Weight-of-evidence exercises 203 Assessing evidence via likelihood ratios 223.1 Likelihood ratios 223.2 The weight-of-evidence formula 243.2.1 Application to the island problem 253.2.2 The population P 253.3 General application of the formula 273.3.1 Several items of evidence 273.3.2 Assessing all the evidence 293.3.3 The role of the expert witness 303.4 Consequences for DNA evidence 313.4.1 Many possible culprits 313.4.2 Incorporating the non-DNA evidence 313.4.3 Relatives 333.4.4 Laboratory and handling errors 343.4.5 Database searches 353.5 Some derivations † 363.5.1 Bayes theorem for identification evidence 373.5.2 Uncertainty about p and N 383.5.3 Grouping the alternative possible culprits 393.5.4 Typing errors 403.6 Further weight-of-evidence exercises 404 Typing technologies 434.1 STR typing 444.1.1 Anomalies 464.1.2 Contamination 494.1.3 Low copy number (LCN) profiling 504.2 mtDNA typing 504.3 Y-chromosome markers 514.4 X-chromosome markers † 524.5 SNP profiles 534.6 Fingerprints † 545 Some population genetics for DNA evidence 565.1 A brief overview 565.1.1 Drift 565.1.2 Mutation 595.1.3 Migration 605.1.4 Selection 605.2 θ, or FST 625.3 A statistical model and sampling formula 635.3.1 Diallelic loci 635.3.2 Multi-allelic loci 685.4 Hardy–Weinberg equilibrium 695.4.1 Testing for deviations from HWE † 705.4.2 Interpretation of test results 745.5 Linkage equilibrium 755.6 Coancestry † 775.7 Likelihood-based estimation of θ † 795.8 Population genetics exercises 816 Identification 826.1 Choosing the hypotheses 826.1.1 Post-data equivalence of hypotheses 846.2 Calculating likelihood ratios 856.2.1 The match probability 856.2.2 One locus 876.2.3 Multiple loci: the “product rule” 896.2.4 Relatives of s 906.2.5 Confidence limits † 926.2.6 Other profiled individuals 936.3 Application to STR profiles 946.3.1 Values for the pj 956.3.2 The value of θ 966.3.3 Errors 986.4 Application to haploid profiles 996.4.1 mtDNA profiles 996.4.2 Y-chromosome markers 1016.5 Mixtures 1016.5.1 Visual interpretation of mixed profiles 1016.5.2 Likelihood ratios under qualitative interpretation 1036.5.3 Quantitative interpretation of mixtures 1086.6 Identification exercises 1097 Relatedness 1117.1 Paternity 1117.1.1 Weight of evidence for paternity 1117.1.2 Prior probabilities 1127.1.3 Calculating likelihood ratios 1137.1.4 Multiple loci: the effect of linkage 1177.1.5 s may be related to c but is not the father 1197.1.6 Incest 1207.1.7 Mother unavailable 1217.1.8 Mutation 1227.2 Other relatedness between two individuals 1267.2.1 Only the two individuals profiled 1267.2.2 Profiled individual close relative of target 1277.2.3 Profiles of known relatives also available † 1287.3 Software for relatedness analyses 1297.4 Inference of ethnicity or phenotype † 1317.5 Relatedness exercises 1338 Other approaches to weight of evidence 1358.1 Uniqueness 1358.1.1 Analysis 1368.1.2 Discussion 1388.2 Inclusion/exclusion probabilities 1388.2.1 Random man 1388.2.2 Inclusion probability of a typing system 1398.2.3 Case-specific inclusion probability 1398.3 Hypothesis testing † 1418.4 Other exercises 1439 Issues for the courtroom 1459.1 Bayesian reasoning in court 1459.2 Some fallacies 1469.2.1 The prosecutor’s fallacy 1469.2.2 The defendant’s fallacy 1479.2.3 The uniqueness fallacy 1489.3 Some UK appeal cases 1489.3.1 Deen (1993) 1489.3.2 Dalby (1995) 1499.3.3 Adams (1996) 1499.3.4 Doheny/Adams (1996) 1519.3.5 Watters (2000) 1539.4 US National Research Council reports 1549.5 Prosecutor’s fallacy exercises 15510 Solutions to exercises 157Bibliography 175Index 183

"This book is a good example of how statistics can be explained in plain English to a nontechnical audience, a skill that every statistician needs to master for improved communication." (Technometrics, August 2008) "...this book should provide a good starting point for any reader..." (International Statistical Institute, January 2006)" … one of the most gifted writers in forensic interpretation…an excellent contribution to our field." (Science & Justice Volume 45 no. 3)