Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

Bayesian Networks

"This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation."
Dr. Ian Evett, Principal Forensic Services Ltd, London, UK

Bayesian Networks
for Probabilistic Inference and Decision Analysis in Forensic Science

Second Edition

Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates diffculties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks.

• Includes self-contained introductions to probability and decision theory.

• Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models.

• Features implementation of the methodology with reference to commercial and academically available software.

• Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases.

• Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning.

• Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them.

• Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background.

• Includes a foreword by Ian Evett.

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.

Autorentext

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

Zusammenfassung
Bayesian Networks This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation.
Dr. Ian Evett, Principal Forensic Services Ltd, London, UK Bayesian Networks
for Probabilistic Inference and Decision Analysis in Forensic Science Second Edition Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates diffculties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks.

• Includes self-contained introductions to probability and decision theory.
• Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models.
• Features implementation of the methodology with reference to commercial and academically available software.
• Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases.
• Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning.
• Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them.
• Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background.
• Includes a foreword by Ian Evett. 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.

Inhalt
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

1.1.1 Probability is not about numbers, it is about coherent reasoning under uncertainty 1

1.1.2 The first two laws of probability 2

1.1.3 Relevance and independence 3

1.1.4 The third law of probability 5

1.1.5 Extension of the conversation 6

1.1.6 Bayes' theorem 6

1.1.7 Probability trees 7

1.1.8 Likelihood and probability 9

1.1.9 The calculus of (probable) truths 10

1.2 Reasoning under uncertainty 12

1.2.1 The Hound of the Baskervilles 12

1.2.2 Combination of background information and evidence 13

1.2.3 The odds form of Bayes' theorem 15

1.2.4 Combination of evidence 16

1.2.5 Reasoning with total evidence 16

1.2.6 Reasoning with uncertain evidence 18

1.3 Population proportions, probabilities and induction 19

1.3.1 The statistical syllogism 19

1.3.2 Expectations and population proportions 21

1.3.3 Probabilistic explanations 22

1.3.4 Abduction and inference to the best explanation 25

1.3.5 Induction the Bayesian way 26

1.4 Decision making under uncertainty 28

1.4.1 Bookmakers in the Courtrooms? 28

1.4.2 Utility theory 29

1.4.3 The rule of maximizing expected utility 33

1.4.4 The loss function 34

1.4.5 Decision trees 35

1.4.6 The expected value of information 38

1.5 Further readings 42

2 The logic of Bayesian networks and influence diagrams 45

2.1 Reasoning with graphical models 45

2.1.1 Beyond detective stories 45

2.1.2 Bayesian networks 46

2.1.3 A graphical model for relevance 48

2.1.4 Conditional independence 50

2.1.5 Graphical models for conditional independence: d-separation 51

2.1.6 A decision rule for conditional independence 53

2.1.7 Networks for evidential reasoning 53

2.1.8 The Markov property 56

2.1.9 Influence diagrams 58

2.1.10 Conditional independence in influence diagrams 60

2.1.11 Relevance and causality 61

2.1.12 The Hound of the Baskervilles revisited 63

2.2 Reasoning with Bayesian networks and influence diagrams 65

2.2.1 Divide and conquer 66

2.2.2 From directed to triangulated graphs 67

2.2.3 From triangulate…