This book explains the correct logical approach to analysis of forensic scientific evidence. The focus is on general methods of analysis applicable to all forms of evidence. It starts by explaining the general principles and then applies them to issues in DNA and other important forms of scientific evidence as examples. Like the first edition, the book analyses real legal cases and judgments rather than hypothetical examples and shows how the problems perceived in those cases would have been solved by a correct logical approach. The book is written to be understood both by forensic scientists preparing their evidence and by lawyers and judges who have to deal with it. The analysis is tied back both to basic scientific principles and to the principles of the law of evidence. This book will also be essential reading for law students taking evidence or forensic science papers and science students studying the application of their scientific specialisation to forensic questions.

Bernard Robertson, Barrister, Inner Temple and New ZealandBernard Robertson is a graduate of Oxford, of the LSE, and of the National Police Staff College, Bramshill as well as being a Barrister of the Inner Temple and of New Zealand. After ten years in the Metropolitan Police, Bernard emigrated to New Zealand and taught the law of evidence at undergraduate and postgraduate levels. He and Professor Vignaux have written numerous papers on Bayesian analysis of scientific evidence and of evidence and court decision making in general. He has also been editor ofThe New Zealand Law Journal and ofThe New Zealand Law Reports, ensuring that he has kept in touch with a wide range of legal issues, including civil litigation.

G. A.Vignaux, Emeritus Professor,?Victoria University, New ZealandG A (Tony) Vignaux (retired) was a physicist and an Operations Research worker, and latterly a Professor of Operations Research at Victoria University. Prior to starting work on legal questions he published on the use of Bayesian methods in physics. With Bernard Robertson he has been invited to address conferences and has been consulted on several legal cases and by enquiries into miscarriage of justice. He has participated in teaching evidence and forensic science to law students at postgraduate level.

Charles Berger, Principal Scientist,?Netherlands Forensic Institute,?The NetherlandsCharles Berger is principal scientist at the Netherlands Forensic Institute (NFI), and professor of Criminalistics at Leiden University. He specializes in subjects such as evidence interpretation and forensic inference. At the NFI he is active in a number of areas such as education and research about which he publishes internationally. He also supports the NFI experts, advises the management and oversees scientific quality. He is involved in promoting logically correct reasoning and concluding, introducing more objective methods, and interpretation at the activity level. For such improvements it is essential to explain them as often and as well as possible to all the stakeholders in the justice system. It is an exciting challenge at the interfaces of the worlds of science, police, and law.

Preface to the First Edition xi

Preface to the Second Edition xv

1. Introduction 1

1.1 Three principles 1

1.2 Dreyfus, Bertillon, and Poincaré 3

1.3 Requirements for Forensic Scientific Evidence 5

1.3.1 Reliability 6

1.4 What We Will Cover 6

2. Interpreting Scientific Evidence 9

2.1 Relevance and Probative Value 9

2.1.1 Ideal and Useless Evidence 10

2.1.2 Typical Evidence 11

2.1.3 An Aside on Probability and Odds 11

2.1.4 A Breath-Testing Device 13

2.2 The Likelihood Ratio and Bayes Theorem 14

2.2.1 The Likelihood Ratio 14

2.2.2 Bayes Theorem 15

2.2.3 The Effect of Prior Odds 16

2.2.4 An HIV Test 16

2.2.5 Transposing the Conditional 17

2.2.6 Giving Evidence 18

2.3 Admissibility and Relevance 19

2.3.1 Prejudging the Case? 20

2.4 Case Studies 21

2.4.1 A Useful Presentation of DNA Evidence 21

2.4.2 The Shoe Mark at the Murder Scene 22

2.4.3 The Probability of Paternity 23

2.4.4 Child Sexual Abuse 26

2.5 Summary 27

3. The Alternative Hypothesis 29

3.1 Some Symbols 29

3.1.1 Hypotheses 29

3.1.2 Evidence 30

3.1.3 Probability 30

3.2 Which Alternative Hypothesis? 30

3.2.1 Probative Value and the Alternative Hypothesis 30

3.2.2 Selecting the Appropriate Alternative Hypotheses 31

3.2.3 Example 32

3.3 Exclusive, Exhaustive, and Multiple Hypotheses 33

3.3.1 Exclusiveness 33

3.3.2 Exhaustiveness 34

3.3.3 Multiple Hypotheses 35

3.4 Immigration and Paternity Cases 35

3.4.1 No Alternative Father 36

3.4.2 A Named Alternative Father 36

3.4.3 An Older Example 37

3.5 It Was My Brother 38

3.6 Traces at the Scene and Traces on the Suspect 39

3.6.1 Traces at the Scene 39

3.6.2 Traces on the Accused 39

3.6.3 The Accuseds Race 40

3.7 Hypothetical Questions 40

3.8 Pre-Trial Conferences and Defence Notice 42

3.9 Case Studies 43

3.9.1 Alternative Hypotheses in Cases of Child Sexual Abuse 43

3.9.2 The Shoe Mark Case Again 43

3.9.3 Sally Clark 44

3.10 Summary 45

4. What Questions Can the Expert Deal With? 47

4.1 The Hierarchy of Propositions 47

4.2 The Ultimate Issue Rule 50

4.2.1 Rationale 51

4.2.2 Experts Must Not Give Evidence on Legal Concepts 51

4.2.3 The Rule and Logical Inference 52

4.2.4 The Ultimate Issue Rule Is Correct 53

4.3 Summary 54

5. Explaining the Strength of Evidence 55

5.1 Explaining the Likelihood Ratio 56

5.1.1 Sensitivity Tables 57

5.2 The Weight of Evidence 57

5.3 Words Instead of Numbers? 58

5.3.1 Standardising Word Meanings 59

5.3.2 The Inconsistent Meanings of Consistent 60

5.3.3 Could Have and Could Have Not 61

5.3.4 Theres Nothing Special about Being Unique 61

5.3.5 Reliability 62

5.3.6 Other Words to Avoid 63

5.4 Dealing with Wrongly Expressed Evidence 63

5.5 Case Studies 64

5.5.1 Shoe Marks 64

5.5.2 Stomach Contents 66

5.5.3 Hair Growth 66

5.6 Summary 67

6. The Case as a Whole 69

6.1 Combining Evidence 69

6.1.1 Dependent and Independent Evidence 70

6.1.2 Conditional Independence 71

6.1.3 Combining Dependent Evidence 72

6.2 Can Combined Weak Evidence Be Stronger Than Its Components? 72

6.3 The Standard of Proof and the Cost of Errors 74

6.3.1 Civil Cases 75

6.3.2 Criminal Cases 75

6.3.3 Child Sex-Abuse Cases 75

6.3.4 Is a Quantifiable Doubt a Reasonable Doubt? 75

6.3.5 What If the Scientific Evidence Is the Only Evidence? 76

6.4 Assessing Prior Odds 76

6.4.1 Prior Odds and the Presumption of Innocence 77

6.5 The Defence Hypothesis and the Prior Odds 78

6.6 Case Studies 78

6.6.1 A Bomb-Hoax Call 78

6.6.2 Loveridge v Adlam 81

6.7 Summary 82

7. Forensic Science Methodology 85

7.1 A General Methodology for Comparative Analysis 86

7.1.1 Choosing Features 86

7.1.2 Choosing How to Compare Features 87

7.1.3 Calculating Same-Source and Different-Source Comparison Scores 88

7.1.4 Generating Likelihood Ratios 90

7.2 Assessing the Performance of an Expert or a Comparison System 90

7.2.1 Discrimination 91

7.2.2 Calibration 91

7.2.3 Misleading Evidence 92

7.2.4 Discrimination versus Calibration 93

7.2.5 Improving Calibration 93

7.3 System Performance Characteristics 95

7.3.1 Tippett Plots 95

7.3.2 Measuring Discrimination and Calibration Separately 96

7.4 Case Assessment and Interpretation (CAI) 98

7.4.1 Defining the Customer Requirement 98

7.4.2 Assessing How Forensic Science Can Help 99

7.4.3 Agreeing on a Case Examination Strategy 99

7.4.4 Examination, Interpretation, and Communication 99

7.4.5 Case Example, Murder or Suicide? 100

7.5 Context Bias 102

7.5.1 Base Rate Information 102

7.5.2 Case Information 103

7.5.3 Reference Material 103

7.5.4 Questioned Material 103

7.6 Summary 104

8. Assigning Likelihood Ratios 107

8.1 DNA 108

8.1.1 A Single Comparison with a Match as a Result 109

8.1.2 A Database Search with a Single Match as a Result 109

8.1.3 A Database Search with Multiple Matches as a Result 110

8.1.4 Extremely Large LRs 111

8.2 Glass Refractive Index 111

8.3 Colour Comparison 113

8.3.1 Colour Feature Selection or Construction 113

8.3.2 Colour Comparison Algorithm 114

8.3.3 Colour Feature and Score Distribution for Collection 114

8.4 Fingerprints 116

8.4.1 Feature Selection or Construction 117

8.4.2 Comparison Algorithm, and Within- and Between-Source Scores 119

8.5 Signatures 121

8.6 Psychological Evidence 125

8.6.1 The Probative Value of Psychological Evidence 125

8.7 Summary 127

9. Errors of Thinking 129

9.1 A Brace of Lawyers Fallacies 129

9.1.1 The Prosecutors Fallacy 129

9.1.2 The Defence Attorneys Fallacy 133

9.1.3 Balance 134

9.2 Double-Counting Evidence? 134

9.3 The Accuracy and Reliability of Scientific Evidence 135

9.3.1 Honest Reporting 136

9.3.2 Quality Control 136

9.3.3 Laboratory Error Rate 137

9.4 Case Studies 138

9.4.1 The mad Earl of Ferrers 138

9.4.2 The Blood on the Belt 139

9.4.3 Broken Glass 141

9.5 Summary 144

10. Frequentist Statistics and Database Matching 147

10.1 The Frequentist Statistical Approach 148

10.1.1 Problems of Significance Testing 148

10.1.2 What Is a Confidence Interval? 150

10.2 Databases 152

10.2.1 Using This Evidence 153

10.2.2 Traps with Databases 153

10.3 The Right Questions and the Wrong Questions 154

10.3.1 When the Wrong Questions Give the Right Answers 155

10.4 Summary 158

11. Implications for the Legal System 161

11.1 What Is Expert Evidence? 161

11.1.1 Is Expert Evidence Just Opinion Evidence? 162

11.1.2 Is Expert Opinion Different from Lay Opinion? 163

11.1.3 Expert Evidence as a Subject in Itself 163

11.2 Who Is an Expert? 164

11.2.1 An Organised Body of Knowledge? 165

11.2.2 Forensic Scientists as Expert Witnesses 166

11.3 Insanity and the Ultimate Issue Rule 166

11.3.1 Is Forensic Science Different from Other Sciences? 168

11.4 Novel Forms of Scientific Evidence 168

11.4.1 Additional Requirements for Forensic Scientific Evidence? 168

11.4.2 The End of the Frye Test Daubert 170

11.4.3 Testing of the Theory or Technique 171

11.4.4 Publication and Peer Review 172

11.4.5 Actual or Potential Error Rates 172

11.4.6 Wide Acceptance 173

11.4.7 Conclusions on Daubert 174

11.5 Knowledge of Context 174

11.5.1 The Importance of Context 174

11.5.2 Defence Disclosure 175

11.6 Court-Appointed Experts 176

11.7 Summary 177

12. Conclusion 179

12.1 Forensic Science as a Science 180

12.2 Conclusions 181

12.3 The Fundamental Questions 181

Appendix 183

A.1 Probability, Odds, Bayes Rule and the Weight of Evidence 183

A.1.1 Probability 183

A.1.2 Odds 184

A.1.3 Symbols 185

A.2 Laws of Probability 186

A.2.1 Complementarity 186

A.2.2 Product Rule 186

A.2.3 Sum Rule 187

A.2.4 The Likelihood Ratio, LR 188

A.2.5 Bayes Rule 188

A.2.6 Probability Form 188

A.2.7 Odds Form of Bayes Rule 189

A.2.8 Combining Evidence 189

A.3 The Weight of Evidence 190

Index 193