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Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science.

By: Contributor(s): Material type: TextTextSeries: Statistics in Practice SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2014Copyright date: ©2014Edition: 2nd edDescription: 1 online resource (473 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118914755
Subject(s): Genre/Form: Additional physical formats: Print version:: Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic ScienceLOC classification:
  • QA279.5 -- .B394 2014eb
Online resources:
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 -- 10.4.3 The value of the findings -- 10.5 Pre-assessment for consignment inspection -- 10.5.1 Inspecting small consignments -- 10.5.2 Bayesian network for inference about small consignments -- 10.5.3 Pre-assessment for inspection of small consignments.
10.6 Pre-assessment for gunshot residue particles.
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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 -- 10.4.3 The value of the findings -- 10.5 Pre-assessment for consignment inspection -- 10.5.1 Inspecting small consignments -- 10.5.2 Bayesian network for inference about small consignments -- 10.5.3 Pre-assessment for inspection of small consignments.

10.6 Pre-assessment for gunshot residue particles.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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