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| Preface | |
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| Foreword | |
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| The logic of uncertainty | |
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| Uncertainty and probability | |
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| Probability is not about numbers | |
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| The first two laws of probability | |
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| Relevance and independence | |
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| The third law of probability | |
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| Extension of the conversation | |
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| Bayes' theorem | |
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| Another look at probability updating | |
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| Likelihood and probability | |
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| The calculus of (probable) truths | |
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| Reasoning under uncertainty | |
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| The Hound of the Baskervilles | |
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| Combination of background information and evidence | |
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| The odds form of Bayes' theorem | |
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| Combination of evidence | |
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| Reasoning with total evidence | |
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| Reasoning with uncertain evidence | |
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| Frequencies and probabilities | |
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| The statistical syllogism | |
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| Expectations and frequencies | |
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| Bookmakers in the Courtrooms? | |
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| Induction and probability | |
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| Probabilistic explanations | |
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| Abduction and inference to the best explanation | |
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| Induction the Bayesian way | |
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| Further readings | |
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| The logic of Bayesian networks | |
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| Reasoning with graphical models | |
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| Beyond detective stories | |
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| What Bayesian networks are and what they can do | |
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| A graphical model for relevance | |
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| Conditional independence | |
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| Graphical models for conditional independence: d-separation | |
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| A decision rule for conditional independence | |
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| Networks for evidential reasoning | |
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| Relevance and causality | |
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| The Hound of the Baskervilles revisited | |
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| Reasoning with Bayesian networks | |
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| 'Jack loved Lulu' | |
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| The Markov property | |
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| Divide and conquer | |
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| From directed to triangulated graphs | |
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| From triangulated graphs to junction trees | |
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| Calculemus | |
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| A probabilistic machine | |
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| Further readings | |
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| General | |
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| Bayesian networks in judicial contexts | |
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| Evaluation of scientific evidence | |
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| Introduction | |
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| The value of evidence | |
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| Relevant propositions | |
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| Source level | |
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| Activity level | |
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| Crime level | |
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| Pre-assessment of the case | |
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| Evaluation using graphical models | |
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| Introduction | |
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| Aspects of constructing Bayesian networks | |
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| Eliciting structural relationships | |
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| Level of detail of variables and quantification of influences | |
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| Derivation of an alternative network structure | |
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| Bayesian networks for evaluating scientific evidence | |
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| Issues in one-trace transfer cases | |
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| Evaluation of the network | |
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| When evidence has more than one component: footwear marks evidence | |
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| General considerations | |
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| Addition of further propositions | |
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| Derivation of the likelihood ratio | |
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| Consideration of distinct components | |
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| A practical example | |
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| An extension to firearm evidence | |
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| A note on the evaluation of the likelihood ratio | |
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| Scenarios with more than one stain | |
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| Two stains, one offender | |
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| Two stains, no putative source | |
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| DNA evidence | |
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| DNA likelihood ratio | |
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| Network approaches to the DNA likelihood ratio | |
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| Missing suspect | |
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| Analysis when the alternative proposition is that a sibling of the suspect left the stain | |
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| Interpretation with more than two propositions | |
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| Evaluation of evidence with more than two propositions | |
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| Partial matches | |
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| Mixtures | |
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| A three-allele mixture scenario | |
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| A Bayesian network | |
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| Relatedness testing | |
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| A disputed paternity | |
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| An extended paternity scenario | |
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| Y-chromosomal analysis | |
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| Database search | |
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| A probabilistic solution to a database search scenario | |
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| A Bayesian network for a database search scenario | |
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| Error rates | |
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| A probabilistic approach to error rates | |
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| A Bayesian network for error rates | |
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| Sub-population and co-ancestry coefficient | |
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| Hardy-Weinberg equilibrium | |
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| Variation in sub-population allele frequencies | |
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| A graphical structure for F[subscript ST] | |
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| DNA likelihood ratio | |
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| Further reading | |
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| Transfer evidence | |
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| Assessment of transfer evidence under crime level propositions | |
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| A single-offender scenario | |
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| A fibre scenario with multiple offenders | |
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| Assessment of transfer evidence under activity level propositions | |
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| Preliminaries | |
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| Derivation of a basic structure for a Bayesian network | |
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| Stain found on a suspect's clothing | |
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| Fibres found on a car seat | |
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| The Background node | |
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| Background from different sources | |
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| A note on the Match node | |
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| A match considered in terms of components y and x | |
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| A structure for a Bayesian network | |
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| Evaluation of the proposed model | |
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| Cross- or two-way transfer of evidential material | |
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| Increasing the level of detail of selected nodes | |
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| Missing evidence | |
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| Determination of a structure for a Bayesian network | |
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| Aspects of the combination of evidence | |
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| Introduction | |
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| A difficulty in combining evidence | |
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| The likelihood ratio and the combination of evidence | |
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| Conditionally independent items of evidence | |
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| Conditionally non-independent items of evidence | |
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| Combination of distinct items of evidence | |
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| Example 1: Handwriting and fingermarks evidence | |
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| Example 2: Issues in DNA analysis | |
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| Example 3: Scenario with one offender and two corresponding items of evidence | |
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| Example 4: Scenarios involving firearms | |
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| Pre-assessment | |
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| Introduction | |
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| Pre-assessment | |
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| Pre-assessment for a fibres scenario | |
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| Preliminaries | |
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| Propositions and relevant events | |
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| Expected likelihood ratios | |
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| Construction of a Bayesian network | |
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| Pre-assessment in a cross-transfer scenario | |
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| Preliminaries | |
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| A Bayesian network for a pre-assessment of a cross-transfer scenario | |
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| The expected weight of evidence | |
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| Pre-assessment with multiple propositions | |
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| Preliminaries | |
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| Construction of a Bayesian network | |
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| Evaluation of different scenarios | |
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| An alternative graphical structure | |
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| Remarks | |
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| Qualitative and sensitivity analyses | |
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| Qualitative probability models | |
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| Qualitative influence | |
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| Additive synergy | |
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| Product synergy | |
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| Properties of qualitative relationships | |
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| Evaluation of indirect influences between separated nodes: a forensic example | |
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| Implications of qualitative graphical models | |
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| Sensitivity analyses | |
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| Sensitivity to a single parameter | |
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| One-way sensitivity analysis based on a likelihood ratio | |
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| A further example of one-way sensitivity analysis | |
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| Sensitivity to two parameters | |
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| Further issues in sensitivity analyses | |
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| Continuous networks | |
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| Introduction | |
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| Samples and estimates | |
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| Measurements | |
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| Summary statistics | |
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| Normal distribution | |
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| Propagation in a continuous Bayesian network | |
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| Propagation in mixed networks | |
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| Example of mixed network | |
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| Use of a continuous distribution which is not normal | |
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| Appendix | |
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| Conditional expectation and variance | |
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| Bayesian network for three serially connected continuous variables | |
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| Bayesian network for a continuous variable with a binary parent | |
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| Bayesian network for a continuous variable with a continuous parent and a binary parent, unmarried | |
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| Further applications | |
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| Offender profiling | |
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| Decision making | |
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| Decision analysis | |
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| Bayesian networks and decision networks | |
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| Forensic decision analyses | |
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| Bibliography | |
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| Author Index | |
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| Subject Index | |