Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science (eBook)

FRANCO TARONI, University of Lausanne, Switzerland ALEX BIEDERMANN, University of Lausanne, Switzerland SILVIA BOZZA, University Ca' Foscari of Venice, Italy PAOLO GARBOLINO, University IUAV of Venice, Italy COLIN AITKEN, University ofEdinburgh, UK

Foreword xiii

Preface to the second edition xvii

Preface to the first edition xxi

1 The logic of decision 1

1.1 Uncertainty and probability 1

1.2 Reasoning under uncertainty 12

1.3 Population proportions, probabilities and induction 19

1.4 Decision making under uncertainty 28

1.5 Further readings 42

2 The logic of Bayesian networks and influence diagrams 45

2.1 Reasoning with graphical models 45

2.2 Reasoning with Bayesian networks and influence diagrams 65

2.3 Further readings 82

3 Evaluation of scientific findings in forensic science 85

3.1 Introduction 85

3.2 The value of scientific findings 86

3.3 Principles of forensic evaluation and relevant propositions 90

3.4 Pre-assessment of the case 100

3.5 Evaluation using graphical models 103

4 Evaluation given source level propositions 113

4.1 General considerations 113

4.2 Standard statistical distributions 115

4.3 Two stains, no putative source 117

4.4 Multiple propositions 122

5 Evaluation given activity level propositions 129

5.1 Evaluation of transfer material given activity level propositions assuming a direct source relationship 130

5.2 Cross- or two-way transfer of trace material 150

5.3 Evaluation of transfer material given activity level propositions with uncertainty about the true source 154

6 Evaluation given crime level propositions 159

6.1 Material found on a crime scene: A general approach 159

6.2 Findings with more than one component: The example of marks 168

6.3 Scenarios with more than one trace: 'Two stain-one offender' cases 182

6.4 Material found on a person of interest 185

7 Evaluation of DNA profiling results 196

7.1 DNA likelihood ratio 196

7.2 Network approaches to the DNA likelihood ratio 198

7.3 Missing suspect 203

7.4 Analysis when the alternative proposition is that a brother of the suspect left the crime stain 206

7.5 Interpretation with more than two propositions 214

7.6 Evaluation with more than two propositions 217

7.7 Partially corresponding profiles 220

7.8 Mixtures 223

7.9 Kinship analyses 227

7.10 Database search 234

7.11 Probabilistic approaches to laboratory error 241

7.12 Further reading 246

8 Aspects of combining evidence 249

8.1 Introduction 249

8.2 A difficulty in combining evidence: The 'problem of conjunction' 250

8.3 Generic patterns of inference in combining evidence 252

8.4 Examples of the combination of distinct items of evidence 262

9 Networks for continuous models 281

9.1 Random variables and distribution functions 281

9.2 Samples and estimates 289

9.3 Continuous Bayesian networks 292

9.4 Mixed networks 306

10 Pre-assessment 314

10.1 Introduction 314

10.2 General elements of pre-assessment 315

10.3 Pre-assessment in a fibre case: A worked through example 316

10.4 Pre-assessment in a cross-transfer scenario 321

10.5 Pre-assessment for consignment inspection 328

10.6 Pre-assessment for gunshot residue particles 335

11 Bayesian decision networks 343

11.1 Decision making in forensic science 343

11.2 Examples of forensic decision analyses 344

11.3 Further readings 368

12 Object-oriented networks 370

12.1 Object orientation 370

12.2 General elements of object-oriented networks 371

12.3 Object-oriented networks for evaluating DNA profiling results 378

13 Qualitative, sensitivity and conflict analyses 388

13.1 Qualitative probability models 389

13.2 Sensitivity analyses 402

13.3 Conflict analysis 410

References 419

Author index 433

Subject index 438

"The clear and accessible style of this second edition
makes this book ideal for all forensic scientists, applied
statisticians and graduate students wishing to evaluate forensic
findings from the perspective of probability and decision
analysis. It will also appeal to lawyers and other scientists and
professionals interested in the evaluation and interpretation of
forensic findings, including decision making based on scientific
information." (Zentralblatt MATH, 1 October
2014)