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

Franco Taroni, Alex Biedermann, Silvia Bozza, Paolo Garbolino, Colin Aitken (Autoren)

eBook Download: EPUB

2014 | 2. Auflage
John Wiley & Sons (Verlag)
978-1-118-91474-8 (ISBN)

Infos

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.

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

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

1.2 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

Rezensionen

"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)

Textauszug

Preface to the second edition

Suppose that you are a forensic scientist, facing a large quantity of information coming from various observations, data or, more generally, findings related to a case under investigation. Your task is to help express a probabilistic conclusion on the joint value of such a quantity items of information or to assist a court of justice in expressing a belief on a judicial question of interest, typically expressed in terms of a proposition, compared to a particular alternative. How should you proceed? Ten years ago, Professor Dennis Lindley wrote in his foreword for another book of two of us (Aitken and Taroni 2004, p. 24):

A problem that arises in a courtroom, affecting both lawyers, witnesses and jurors, is that several pieces of evidence have to be put together before a reasoned judgement can be reached: as when motive has to be considered along with material evidence. Probability is designed to effect such combinations but the accumulation of simple rules can produce complicated procedures. Methods of handling sets of evidence have been developed: for example Bayes nets (...). There is a fascinating interplay here between the lawyer and the scientist where they can learn from each other and develop tools that significantly assist in the production of a better judicial system.

Indeed, during the past three decades, the so-called Bayesian networks have gradually become a centre of attention for researchers from several academic fields. Whenever complicated inference problems involving uncertainty as a characterizing feature need to be captured and approached in a coherent way, that is using the normative framework of probability, their clarity of formulation and thorough computational architecture can provide a level of assistance that in many fields is unprecedented, in particular when there is a need to associate a reasoning process with a wider context of decision analysis and decision making.

As pointed out in forensic science and judicial literature, the merit of the Bayesian network graphical probability environment goes well beyond a purely descriptive account that focusses on the translation of a reasoner's view of a particular inference problem of interest. On the one hand, Bayesian networks support the concise description of challenging practical problems and the communication of their essential features so as to favour their understanding amongst discussants. On the other hand, Bayesian networks extend to a dynamic dimension that provides a means for belief computations; that is, the revision of a reasoner's belief structure as a result of knowing the truth or otherwise of one or more propositions that are part of the description of the overall problem. One of the very strengths of Bayesian networks is that their users can concentrate their efforts on eliciting sensible network structures and probability assignments, while leaving the computational burden to computerized implementations of Bayesian network models. However, there is no claim here of a ‘true’ model: indeed, different analysts may come up with different models for the same problem. Definitions of basic entities, the specification of their relationships and probability assignments may naturally differ because different analysts may hold different background information and may have different views of how a particular problem ought to be understood. However, this is not a drawback of the Bayesian network modelling language; it is one of its very strengths to make such differences explicit and provide a transparent framework for exploring the nature and extent of these differences. With respect to the theory of Bayesian networks, this amounts to applied research, but with respect to forensic science, such research is fundamental because it can provide original and innovative insights.

Inference and decision analysis, supported by Bayesian networks, should help us to acquire a better understanding of the problem we face, in terms of the target propositions of interest, our uncertainties about their true state and the way in which new items of information ought to affect our view. This better understanding can help to place scientists in a more secure position when they are required to advise other participants in the legal process on issues concerning the evaluation of forensic results. Typical questions include, but are not limited to: What is the bearing this finding has on this proposition, as compared to a given alternative proposition? If so, to what extent can we affirm degree of support? Should we attempt to acquire further information? If so, which other information?

One point that is clear from these introductory thoughts is that there are no pre-defined solutions. Bayesian networks are an abstract concept, and besides some aspects of definition that prescribe particular modelling constraints, there is nothing in the concept as such to tell us how to define sensible Bayesian network structures. This places forensic scientists in a responsible position: they need to make up their minds seriously and invoke further argument to justify particular model structures and their relevance for particular contexts of application. Like probability, Bayesian networks are both a very strict and a very liberal concept. They require the analyst to observe a few general principles of probabilistic reasoning, but beyond this, there are no prescriptions of as to how the basic terms ought to be interpreted. This highlights the personal nature of the approach, for which Bayesian analysis in general is so well known.

At the same time, this paradigm leads directly to one of the main motivations for a book on Bayesian networks for forensic science. It is driven by the question of how forensic scientists may use Bayesian networks meaningfully in their work. The idea thus is to offer the reader a guided introduction to the use of Bayesian networks for analysing forensic inference problems that arise in connection with various types of traces. To convince the reader that Bayesian networks can be specified in a defensible way, it is useful to point out that they can capture and illustrate the rationale behind particular probabilistic solutions, notably likelihood ratio formulae described in existing literature, which are now generally accepted as a measure of probative value. This is illustrated through various examples given throughout this book with reference to the original literature. The aim is to clarify the logic of generic structures of inferential networks that readers may transfer to their own contexts of application. Often, original literature provides numerical examples based on scenarios inspired by real cases that will allow the reader to track particular numerical output (Evett et al. 1998b).

Descriptions and analyses of entire real cases demand a substantial amount of additional discussion and explanation, in particular with respect to numerical specification. This would have clearly exceeded the space available in this book. The subtlety of real case analysis is illustrated, for example, by a whole book by Kadane and Schum (1996) devoted to the Sacco and Vanzetti case and papers covering selected case studies by Biedermann et al. (2011b); Evett et al. (2002). For a book with chapters focusing on selected practical applications from different fields –not necessarily forensic – see, for example, Pourret et al. (2008).

The second edition of this book on Bayesian networks features a series of changes. The theoretical introduction offered by Chapters 1 and 2 on probability and inference has been extended with material related to decision theory and its application. The reason for this is that scientists, but most importantly Courts of Justice, must reach decisions on the basis of particular items of information. In this context, Bayesian decision networks allow one to describe a general framework for logical decision analysis (and, hence, decision making) and how graphical models can support coherent decision making. In addition, aspects of terminology related to object-oriented Bayesian networks, a concept to support advanced graphical modelling, have been added.

Chapters 3–6 lay out the logic of forensic evaluation given the established levels of propositions known as source, activity and crime (or offense), respectively. Each level has its own particular features, although there are connections between them, and Bayesian networks are an excellent means by which these can be made explicit. The discussion with respect to the various levels of propositions is kept separate in order to ease the understanding. This structure allows the reader to see the impact of an increased number of variables and their effect on inferential tasks. A note on the use of standard statistical distributions to define node tables, as offered by some Bayesian network software, is also included.

Evaluation of DNA profiling results is presented in Chapter 7, with new material on database searching and ways to account for the probability of (laboratory) error. Chapter 8 relates to the challenging topic of the joint value of multiple items of evidence. It covers material on the foundational aspects of such assessment given by Professor David Schum's pioneering works [Schum (1994)]. In turn, Chapter 9 deals with the use of continuous variables for Bayesian network construction, including both continuous and mixed networks with examples of applications.

Chapter 10 on ‘Pre-assessment’ introduces new sections on consignment inspection (i.e. sampling) and gunshot residues particles, followed by an entirely new Chapter 11, focusing on how Bayesian networks can be logically extended to incorporate...

Produkt-Details

• Erscheint lt. Verlag: 21.7.2014
• Reihe/Serie: Statistics in Practice
• Reihe/Serie: Statistics in Practice
• Reihe/Serie: Statistics in Practice
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Recht / Steuern ► Strafrecht ► Kriminologie
• Themenwelt: Sozialwissenschaften
• Themenwelt: Technik
• Schlagworte: Angewandte Wahrscheinlichkeitsrechnung u. Statistik • Applied Probability & Statistics • Statistics • Statistik
• ISBN-10: 1-118-91474-0 / 1118914740
• ISBN-13: 978-1-118-91474-8 / 9781118914748