Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science.
Title:
Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science.
Author:
Taroni, Franco.
ISBN:
9781118914755
Personal Author:
Edition:
2nd ed.
Physical Description:
1 online resource (473 pages)
Series:
Statistics in Practice
Contents:
Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface to the second edition -- Preface to the first edition -- Chapter 1 The logic of decision -- 1.1 Uncertainty and probability -- 1.1.1 Probability is not about numbers, it is about coherent reasoning under uncertainty -- 1.1.2 The first two laws of probability -- 1.1.3 Relevance and independence -- 1.1.4 The third law of probability -- 1.1.5 Extension of the conversation -- 1.1.6 Bayes' theorem -- 1.1.7 Probability trees -- 1.1.8 Likelihood and probability -- 1.1.9 The calculus of (probable) truths -- 1.2 Reasoning under uncertainty -- 1.2.1 The Hound of the Baskervilles -- 1.2.2 Combination of background information and evidence -- 1.2.3 The odds form of Bayes' theorem -- 1.2.4 Combination of evidence -- 1.2.5 Reasoning with total evidence -- 1.2.6 Reasoning with uncertain evidence -- 1.3 Population proportions, probabilities and induction -- 1.3.1 The statistical syllogism -- 1.3.2 Expectations and population proportions -- 1.3.3 Probabilistic explanations -- 1.3.4 Abduction and inference to the best explanation -- 1.3.5 Induction the Bayesian way -- 1.4 Decision making under uncertainty -- 1.4.1 Bookmakers in the Courtrooms? -- 1.4.2 Utility theory -- 1.4.3 The rule of maximizing expected utility -- 1.4.4 The loss function -- 1.4.5 Decision trees -- 1.4.6 The expected value of information -- 1.5 Further readings -- Chapter 2 The logic of Bayesian networks and influence diagrams -- 2.1 Reasoning with graphical models -- 2.1.1 Beyond detective stories -- 2.1.2 Bayesian networks -- 2.1.3 A graphical model for relevance -- 2.1.4 Conditional independence -- 2.1.5 Graphical models for conditional independence: d-separation -- 2.1.6 A decision rule for conditional independence -- 2.1.7 Networks for evidential reasoning -- 2.1.8 The Markov property.
2.1.9 Influence diagrams -- 2.1.10 Conditional independence in influence diagrams -- 2.1.11 Relevance and causality -- 2.1.12 The Hound of the Baskervilles revisited -- 2.2 Reasoning with Bayesian networks and influence diagrams -- 2.2.1 Divide and conquer -- 2.2.2 From directed to triangulated graphs -- 2.2.3 From triangulated graphs to junction trees -- 2.2.4 Solving influence diagrams -- 2.2.5 Object-oriented Bayesian networks -- 2.2.6 Solving object-oriented Bayesian networks -- 2.3 Further readings -- 2.3.1 General -- 2.3.2 Bayesian networks and their predecessors in judicial contexts -- Chapter 3 Evaluation of scientific findings in forensic science -- 3.1 Introduction -- 3.2 The value of scientific findings -- 3.3 Principles of forensic evaluation and relevant propositions -- 3.3.1 Source level propositions -- 3.3.1.1 Notation -- 3.3.1.2 Single stain -- 3.3.2 Activity level propositions -- 3.3.2.1 Notation and formulaic development -- 3.3.3 Crime level propositions -- 3.3.3.1 Notation -- 3.3.3.2 Association propositions -- 3.3.3.3 Intermediate association propositions -- 3.4 Pre-assessment of the case -- 3.5 Evaluation using graphical models -- 3.5.1 Introduction -- 3.5.2 General aspects of the construction of Bayesian networks -- 3.5.3 Eliciting structural relationships -- 3.5.4 Level of detail of variables and quantification of influences -- 3.5.5 Deriving an alternative network structure -- Chapter 4 Evaluation given source level propositions -- 4.1 General considerations -- 4.2 Standard statistical distributions -- 4.3 Two stains, no putative source -- 4.3.1 Likelihood ratio for source inference when no putative source is available -- 4.3.2 Bayesian network for a two-trace case with no putative source.
4.3.3 An alternative network structure for a two trace no putative source case -- 4.4 Multiple propositions -- 4.4.1 Form of the likelihood ratio -- 4.4.2 Bayesian networks for evaluation given multiple propositions -- 4.4.2.1 Model 1 -- 4.4.2.2 Model 2 -- 4.4.2.3 Model 3 -- Chapter 5 Evaluation given activity level propositions -- 5.1 Evaluation of transfer material given activity level propositions assuming a direct source relationship -- 5.1.1 Preliminaries -- 5.1.2 Derivation of a basic structure for a Bayesian network -- 5.1.3 Modifying the basic network -- 5.1.4 Further considerations about background presence -- 5.1.5 Background from different sources -- 5.1.6 An alternative description of the findings -- 5.1.7 Bayesian network for an alternative description of findings -- 5.1.8 Increasing the level of detail of selected propositions -- 5.1.9 Evaluation of the proposed model -- 5.2 Cross- or two-way transfer of trace material -- 5.3 Evaluation of transfer material given activity level propositions with uncertainty about the true source -- 5.3.1 Network structure -- 5.3.2 Evaluation of the network -- 5.3.3 Effect of varying assumptions about key factors -- Chapter 6 Evaluation given crime level propositions -- 6.1 Material found on a crime scene: A general approach -- 6.1.1 Generic network construction for single offender -- 6.1.2 Evaluation of the network -- 6.1.3 Extending the single-offender scenario -- 6.1.4 Multiple offenders -- 6.1.5 The role of the relevant population -- 6.2 Findings with more than one component: The example of marks -- 6.2.1 General considerations -- 6.2.2 Adding further propositions -- 6.2.3 Derivation of the likelihood ratio -- 6.2.4 Consideration of distinct components -- 6.2.5 An extension to firearm examinations -- 6.2.6 A note on the likelihood ratio.
6.3 Scenarios with more than one trace: 'Two stain-one offender' cases -- 6.4 Material found on a person of interest -- 6.4.1 General form -- 6.4.2 Extending the numerator -- 6.4.3 Extending the denominator -- 6.4.4 Extended form of the likelihood ratio -- 6.4.5 Network construction and examples -- Chapter 7 Evaluation of DNA profiling results -- 7.1 DNA likelihood ratio -- 7.2 Network approaches to the DNA likelihood ratio -- 7.2.1 The 'match' approach -- 7.2.2 Representation of individual alleles -- 7.2.3 Alternative representation of a genotype -- 7.3 Missing suspect -- 7.4 Analysis when the alternative proposition is that a brother of the suspect left the crime stain -- 7.4.1 Revision of probabilities and networks -- 7.4.2 Further considerations on conditional genotype probabilities -- 7.5 Interpretation with more than two propositions -- 7.6 Evaluation with more than two propositions -- 7.7 Partially corresponding profiles -- 7.8 Mixtures -- 7.8.1 Considering multiple crime stain contributors -- 7.8.2 Bayesian network for a three-allele mixture scenario -- 7.9 Kinship analyses -- 7.9.1 A disputed paternity -- 7.9.2 An extended paternity scenario -- 7.9.3 A case of questioned maternity -- 7.10 Database search -- 7.10.1 Likelihood ratio after database searching -- 7.10.2 An analysis focussing on posterior probabilities -- 7.11 Probabilistic approaches to laboratory error -- 7.11.1 Implicit approach to typing error -- 7.11.2 Explicit approach to typing error -- 7.12 Further reading -- 7.12.1 A note on object-oriented Bayesian networks -- 7.12.2 Additional topics -- Chapter 8 Aspects of combining evidence -- 8.1 Introduction -- 8.2 A difficulty in combining evidence: The 'problem of conjunction' -- 8.3 Generic patterns of inference in combining evidence -- 8.3.1 Preliminaries.
8.3.2 Dissonant evidence: Contradiction and conflict -- 8.3.2.1 Contradiction -- 8.3.2.2 Conflict -- 8.3.3 Harmonious evidence: Corroboration and convergence -- 8.3.3.1 Corroboration -- 8.3.3.2 Convergence -- 8.3.4 Drag coefficient -- 8.4 Examples of the combination of distinct items of evidence -- 8.4.1 Handwriting and fingermarks -- 8.4.2 Issues in DNA analyses -- 8.4.3 One offender and two corresponding traces -- 8.4.4 Firearms and gunshot residues -- 8.4.4.1 Marks present on fired bullets -- 8.4.4.2 Gunshot residues -- 8.4.4.3 Bayesian network for evaluating residue particles -- 8.4.4.4 Combining results of comparative examinations of marks and visualized gunshot residues -- 8.4.5 Comments -- Chapter 9 Networks for continuous models -- 9.1 Random variables and distribution functions -- 9.1.1 Normal distribution -- 9.1.2 Bivariate Normal distribution -- 9.1.3 Conditional expectation and variance -- 9.2 Samples and estimates -- 9.2.1 Summary statistics -- 9.2.2 The Bayesian paradigm -- 9.3 Continuous Bayesian networks -- 9.3.1 Propagation in a continuous Bayesian network -- 9.3.2 Background data -- 9.3.3 Intervals for a continuous entity -- 9.4 Mixed networks -- 9.4.1 Bayesian network for a continuous variable with a discrete parent -- 9.4.2 Bayesian network for a continuous variable with a continuous parent and a binary parent, unmarried -- Chapter 10 Pre-assessment -- 10.1 Introduction -- 10.2 General elements of pre-assessment -- 10.3 Pre-assessment in a fibre case: A worked through example -- 10.3.1 Preliminaries -- 10.3.2 Propositions and relevant events -- 10.3.3 Expected likelihood ratios -- 10.3.4 Construction of a Bayesian network -- 10.4 Pre-assessment in a cross-transfer scenario -- 10.4.1 Bidirectional transfer.
10.4.2 A Bayesian network for a pre-assessment of a cross-transfer scenario.
Abstract:
"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 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 difficulties 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..
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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Electronic Access:
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