Weight-of-Evidence for Forensic DNA Profiles

David J. Balding, University of Melbourne, Australia; and University College London, UK.Christopher D. Steele, University College London, UK.

• Preface to the 2nd edition xviPreface to the 1st edition xvii1 Introduction 11.1 Weight-of-evidence theory 11.2 About the book 31.3 DNA profiling technology 41.4 What you need to know already 51.5 Other resources 62 Crime on an island 92.1 Warm-up examples 102.1.1 People v. Collins (California, 1968) 102.1.2 Disease testing: Positive Predictive Value (PPV) 102.1.3 Coloured taxis 122.2 Rare trait identification evidence 142.2.1 The \island" problem 142.2.2 A first lesson from the island problem 152.3 Making the island problem more realistic 172.3.1 The effect of uncertainty about p 172.3.2 Uncertainty about N 192.3.3 The effect of possible typing errors 192.3.4 The effect of searches 202.3.5 The effect of other evidence 222.3.6 The effects of relatives and population subdivision 232.4 Weight-of-evidence exercises 243 Assessing evidence using likelihoods 273.1 Likelihoods and their ratios 283.2 The weight-of-evidence formula 293.2.1 Application to the island problem 313.3 General application of the formula 323.3.1 Several items of evidence 323.3.2 The role of the expert witness 343.4 Consequences for DNA evidence 353.4.1 Many possible culprits 353.4.2 Incorporating the non-DNA evidence 353.4.3 Relatives 383.4.4 Laboratory and handling errors 393.4.5 Database searches 403.5 Derivation of the weight-of-evidence formula y 423.5.1 Bayes Theorem 423.5.2 Uncertainty about p and N 433.5.3 Grouping the alternative possible culprits 443.5.4 Typing errors 453.6 Further weight-of-evidence exercises 464 Profiling technologies 494.1 STR typing 504.1.1 Anomalies 534.1.2 Contamination 564.1.3 Low-template DNA (LTDNA) profiling 564.2 mtDNA typing 584.3 Y-chromosome markers 594.4 X-chromosome markers † 594.5 SNP profiles † 604.6 Sequencing † 624.7 Methylation † 624.8 RNA † 634.9 Fingerprints † 635 Some population genetics for DNA evidence 655.1 A brief overview 655.1.1 Drift 655.1.2 Mutation 685.1.3 Migration 695.1.4 Selection 705.2 FST 715.2.1 Population genotype probabilities 735.3 A statistical model and sampling formula 745.3.1 Diallelic loci 745.3.2 Multi-allelic loci 795.4 Hardy-Weinberg equilibrium 805.4.1 Testing for deviations from HWE † 815.4.2 Interpretation of test results 865.5 Linkage equilibrium 865.6 Coancestry † 885.7 Likelihood-based estimation of FST † 905.8 Population genetics exercises 926 Inferences of identity 956.1 Choosing the hypotheses 956.1.1 Post-data equivalence of hypotheses 976.2 Calculating LRs 996.2.1 The match probability 996.2.2 Single locus 1006.2.3 Multiple loci: the \product rule" 1036.2.4 Relatives of Q 1056.2.5 Confidence limits † 1076.2.6 Other profiled individuals 1086.3 Application to STR profiles 1096.3.1 Values for the pj 1096.3.2 The value of FST 1116.3.3 Choice of population 1126.3.4 Errors 1136.4 Application to haploid profiles 1146.4.1 mtDNA profiles 1146.4.2 Y-chromosome markers 1166.5 Mixtures 1176.5.1 Visual interpretation of mixed profiles 1176.5.2 Likelihood ratios under qualitative interpretation 1196.5.3 Quantitative interpretation of mixtures 1246.6 Identification exercises 1267 Inferring relatedness 1297.1 Paternity 1297.1.1 Weight of evidence for paternity 1297.1.2 Prior probabilities 1307.1.3 Calculating LRs 1317.1.4 Multiple loci: the effect of linkage 1367.1.5 Q may be related to c but not the father 1387.1.6 Incest 1397.1.7 Mother unavailable 1407.1.8 Mutation 1417.2 Other relatedness between two individuals 1467.2.1 Only the two individuals profiled 1467.2.2 Profiles of known relatives also available y 1477.2.3 Software for relatedness analyses 1487.3 Familial search 1507.4 Inference of ethnicity y 1517.5 Inference of phenotype y 1537.6 Relatedness exercises 1538 Low template DNA profiles 1558.1 Background 1558.2 Stochastic effects in LTDNA profiles 1588.2.1 Dropout 1588.2.2 Dropin 1588.2.3 Peak Imbalance 1598.2.4 Stutter 1598.3 Computing likelihoods 1608.3.1 Single contributor allowing for dropout 1608.3.2 Profiled contributors not subject to dropout 1618.3.3 Modelling dropin 1628.3.4 Multi-dose dropout and degradation 1638.3.5 Additional contributors subject to dropout 1648.3.6 Replicates 1648.3.7 Using peak heights 1658.4 Quality of results 1689 Introduction to likeLTD† 1719.1 Installation and example R script 1729.1.1 Input 1729.1.2 Allele report 1739.1.3 Arguments and optimisation 1739.1.4 Output report 1759.1.5 Genotype probabilities 1779.2 Specifics of the package 1799.2.1 The parameters 1799.2.2 Key features of likeLTD 1809.2.3 Maximising the penalised likelihood 1819.2.4 Computing time and memory requirements 1829.3 Verification 18310 Other approaches to weight of evidence 18710.1 Uniqueness 18810.1.1 Analysis 18910.1.2 Discussion 19010.2 Inclusion/Exclusion probabilities 19010.3 Hypothesis Testing y 19310.4 Other exercises 19411 Some issues for the courtroom 19711.1 The role of the expert witness 19711.2 Bayesian reasoning in court 19811.3 Some fallacies 20011.3.1 The prosecutor's fallacy 20011.3.2 The defendant's fallacy 20111.3.3 The uniqueness fallacy 20111.4 Some UK appeal cases 20211.4.1 Deen (1993) 20211.4.2 Adams (1996) 20211.4.3 Doheny/Adams (1996) 20411.4.4 Watters (2000) 20611.4.5 T (2010) 20711.4.6 Dlugosz (2013) 20911.5 US National Research Council reports 21011.6 Prosecutor's fallacy exercises 21212 Solutions to exercises 213