Franco Taroni - Statistics and the Evaluation of Evidence for Forensic Scientists

1 Cover

2 Wiley Series in Statistics in Practice

3 Statistics and the Evaluation of Evidence for Forensic Scientists

4 Copyright

5 Dedication

6 Foreword

7 Preface to Third Edition

8 Preface to Second Edition Note

9 1 Uncertainty in Forensic Science 1.1 Introduction 1.2 Statistics and the Law 1.3 Uncertainty in Scientific Evidence 1.4 Terminology 1.5 Types of Data 1.6 Populations 1.7 Probability Notes

10 2 The Evaluation of Evidence 2.1 Odds 2.2 Bayes' Theorem 2.3 The Odds Form of Bayes' Theorem 2.4 The Value of Evidence 2.5 Errors in Interpretation 2.6 Misinterpretations 2.7 Explanation of Transposed Conditional, Defence Attorney's and False Positive Fallacies 2.8 Making Coherent Decisions 2.9 Graphical Probabilistic Models: Bayesian Networks Notes

11 3 Historical Review 3.1 Early History 3.2 The Dreyfus Case 3.3 Statistical Arguments by Early Twentieth‐Century Forensic Scientists 3.4 People v . Collins 3.5 Discriminating Power 3.6 Significance Probabilities 3.7 Coincidence Probabilities 3.8 Likelihood Ratio Notes

12 4 Bayesian Inference 4.1 Introduction 4.2 Inference for a Proportion 4.3 Sampling 4.4 Bayesian Networks for Sampling Inspection 4.5 Inference for a Normal Mean 4.6 Quantity Estimation 4.7 Decision Analysis Notes

13 5 Evidence and Propositions: Theory5.1 The Choice of Propositions and Pre‐Assessment 5.2 Levels of Propositions and Roles of the Forensic Scientist 5.3 The Formal Development of a Likelihood Ratio for Different Propositions and Discrete Characteristics 5.4 Validation of Bayesian Network Structures: An Example 5.5 Pre‐Assessment 5.6 Combination of Items of Evidence Notes

14 6 Evidence and Propositions: Practice 6.1 Examples for Evaluation given Source Level Propositions 6.2 Examples for Evaluation given Activity Level Propositions 6.3 Examples for Evaluation given Offence Level Propositions 6.4 Summary Notes

15 7 Data Analysis7.1 Introduction 7.2 Theory for Discrete Data 7.3 Theory for Continuous Univariate Data 7.4 Normal Between‐Source Variation 7.5 Non‐normal Between‐Source Variation 7.6 Multivariate Analysis 7.7 Discrimination 7.8 Score‐Based Models 7.9 Bayes' Factor and Likelihood Ratio (cont.) Notes

16 8 Assessment of the Performance of Methods for the Evaluation of Evidence 8.1 Introduction 8.2 Properties of Methods for Evaluation 8.3 General Topics Relating to Sample Size Estimation and to Assessment 8.4 Assessment of Performance of a Procedure for the Calculation of the Likelihood Ratio 8.5 Case Study: Kinship Analysis 8.6 Conclusion Notes

17 A AProbability DistributionsProbability Distributions A.1 Introduction A.2 Probability Distributions for Counts A.3 Measurements Notes

18 B BMatrix PropertiesMatrix PropertiesB.1 Matrix Terminology

19 References

20 1 Notation

21 Cases

22 Author Index

23 Subject Index

24 End User License Agreement

1 Chapter 1 Table 1.1 Genotypic relative frequencies for locus LDLR amongst Caucasians in ... Table 1.2 Refractive index measurements. Table 1.3 Presence and absence of diffuse vascular injuries (DVI) and diffuse... Table 1.4 Genotype probabilities, assuming Hardy–Weinberg equilibrium, for a ...

2 Chapter 2 Table 2.1 Two‐by‐two contingency table for frequencies for the tabulation of ... Table 2.2 Two‐by‐two contingency table for probabilities for the tabulation o... Table 2.3 Two‐by‐two contingency table for artificial frequencies for the tab... Table 2.4 Hypothetical results for deaths amongst a population. Table 2.5 Frequency of fingerprint characteristics by gender and handedness e... Table 2.6 Effect on prior odds in favour of relative to of evidence with... Table 2.7 Value of the evidence for each genotype, given genotypic relative f... Table 2.8 Qualitative scale for reporting the value V of the support of the ev... Table 2.9 Verbal scale of support for a null hypothesis NH proposed by Jeffr... Table 2.10 Verbal scale of support for a likelihood ratio proposed by Nordga... Table 2.11 The values of the logarithm of the posterior odds in favour of an ...Table 2.12 Probability of at least one match, given a relative frequency of ...Table 2.13 Evidence occurs with .Table 2.14 The probability, , of at least one match with the evidence, which ...Table 2.15 The ‘ ’ loss function, for .Table 2.16 Loss function for the Bayesian decision network shown in Figure 2....

3 Chapter 3Table 3.1 Probabilities for various characteristics of the couple observed in...Table 3.2 Allelic frequencies for TPOX locus for Swiss and NZ Caucasians and ...Table 3.3 Allelic frequencies for TH01 locus for Swiss and NZ Caucasians and ...Table 3.4 Significance probabilities for refractive index of glass for mea...Table 3.5 Variation in the likelihood ratio , as given by (3.7), with sample ...

4 Chapter 4Table 4.1 Probability that the proportion of drugs in a large consignment is ...Table 4.2 The sample size required to be % certain that the proportion of uni...Table 4.3 Probabilities all inspected units contain drugs for in a populat...Table 4.4 Definitions of nodes used in the Bayesian network shown in Figure 4...Table 4.5 Definitions of nodes used in the Bayesian networks shown in Figure ...Table 4.6 Estimates of quantities of drugs, in a consignment of units, acc...Table 4.7 Estimates of quantities of drugs, in a consignment of units, acc...Table 4.8 Sensitivity of the optimal decision on the alcohol level (g/kg) to ...Table 4.9 Definitions of the nodes used in the influence diagram shown in Fig...