Probability and forensic evidence : theory, philosophy, and applications / Ronald Meester, Klaas Slooten.

Format:

Book

Author/Creator:

Meester, Ronald, author.

Slooten, Klaas, author.

Language:

English

Subjects (All):

Forensic statistics.

Physical Description:

1 online resource (xii, 442 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

This book addresses the role of statistics and probability in the evaluation of forensic evidence, including both theoretical issues and applications in legal contexts. It discusses what evidence is and how it can be quantified, how it should be understood, and how it is applied (and, sometimes, misapplied). After laying out their philosophical position, the authors begin with a detailed study of the likelihood ratio. Following this grounding, they discuss applications of the likelihood ratio to forensic questions, in the abstract and in concrete cases. The analysis of DNA evidence in particular is treated in great detail. Later chapters concern Bayesian networks, frequentist approaches to evidence, the use of belief functions, and the thorny subject of database searches and familial searching. Finally, the authors provide commentary on various recommendation reports for forensic science. Written to be accessible to a wide audience of applied mathematicians, forensic scientists, and scientifically-oriented legal scholars, this book is a must-read for all those interested in the mathematical and philosophical foundations of evidence and belief.

Contents:

Cover

Half-title

Title page

Copyright information

Contents

Preface

1 Some Philosophy of Probability, Statistics, and Forensic Science

1.1 The Kolmogorov Axioms of Probability

1.2 The Frequentistic Interpretation

1.3 The Inadequacy of Relative Frequencies in the Legal and Forensic Context

1.4 Epistemic Probability

1.5 Problems and Anomalies

1.6 An Example: DNA Profiles

1.7 Statistics

1.7.1 Statistical Evidence

1.8 Forensic Science

1.9 Summary and Conclusions

1.10 Bibliographical Notes

2 Evidence and the Likelihood Ratio

2.1 From Evidence to Likelihood Ratio

2.2 Further Examples of Likelihood Ratios

2.2.1 Combination of Evidence

2.3 The Likelihood Ratio Meets Necessary Requirements

2.3.1 Dependence on Probabilities of Observed Data Only

2.3.2 Irrelevance of the Experimental Setup

2.4 The Distribution of the Likelihood Ratio

2.4.1 Basic Properties of the Likelihood Ratio Distribution

2.4.2 Misleading Evidence

2.4.3 Behavior Under Repeated Experiments

2.4.4 Asymmetry of the Likelihood Ratio Distributions

2.4.5 The Weight of the Evidence

2.4.6 Likelihood Ratio Versus Weight of Evidence

2.5 Summary and Conclusions

2.6 Bibliographical Notes

3 The Uncertainty of the Likelihood Ratio

3.1 The Nature of the Likelihood Ratio

3.2 A Concrete Example

3.3 The Posterior Likelihood Ratio Distribution

3.4 Examples of Posterior Likelihood Ratio Distributions

3.4.1 Continuation of Example 3.2.1

3.4.2 DNA Mixtures

3.4.3 Height Measurements

3.5 Summary and Conclusions

3.6 Bibliographical Notes

4 Forensic Identification

4.1 The Classical Case

4.2 The Effect of a Search

4.3 Uncertainty About p

4.4 The Existence of Subpopulations

4.5 Some Examples and Special Cases

4.5.1 Characteristic Rare in Other Populations.

4.5.2 S is the Only Candidate in its Subpopulation

4.5.3 Autosomal DNA Profiles

4.5.4 Uniform Priors

4.5.5 Hypotheses Using the Evidence

4.5.6 Parental Identification

4.6 Which Likelihood Ratio?

4.7 Uncertainty or Measurement Error of the Evidence

4.8 Summary and Conclusions

4.9 Bibliographical Notes

5 The Bayesian Framework in Legal Cases

5.1 The Link Hammer Case

5.2 Examples of Combination of Evidence

5.3 The Sally Clark Case

5.4 The Death of the Linesman

5.5 The Lucia de Berk Case

5.5.1 A Naive Likelihood Approach

5.5.2 Naive Bayes - A Short Detour

5.5.3 Are There Better Statistical Approaches?

5.6 The Case of the Information Telephone

5.7 Two Burglary Cases

5.7.1 A Case with Several Weak Pieces of Evidence

5.7.2 A Burglary Case in Rotterdam

5.8 Summary and Conclusions

5.9 Bibliographical Notes

6 Bayesian Networks

6.1 The Basics

6.2 Conditional Independence

6.3 Some Examples of Bayesian Networks

6.3.1 Evaluation of a Matching Characteristic

6.3.2 The Jury Fallacy

6.3.3 The Simonshaven Case

6.4 Modeling Competing Arguments with a Bayesian Network

6.4.1 Splitting the Hypothesis Node

6.4.2 Starting with Different Hypotheses Nodes

6.5 Bayesian Network Selection

6.6 Summary and Conclusions

6.7 Bibliographical Notes

7 DNA

7.1 Forensic DNA Profiling

7.2 Population Frequencies Versus Profile Probabilities

7.3 Uncertainty About Allele Frequencies: The DirichletDistribution

7.4 Match Probabilities

7.5 Population Genetics and the θ-Correction

7.5.1 The General Allele Sampling Formula in the IBD Interpretation

7.5.2 The θ-Correction in Forensic Practice

7.6 Kinship

7.6.1 The Inbreeding Coefficient of an Individual

7.6.2 Computing the Coancestry Coefficient for Non-inbred Individuals.

7.6.3 Likelihood Ratios for Pairwise Relatedness

7.6.4 Expectation of the Likelihood Ratio for Pairwise Kinship

7.6.5 Linked Loci

7.6.6 Likelihood Ratio and Weight of Evidence

7.7 Summary and Conclusions

7.8 Bibliographical Notes

8 Statistical Modeling and DNA Mixture Evaluation

8.1 Mixture Likelihood Ratios

8.1.1 Mixture Models, Abstractly

8.1.2 Explicit Examples

8.1.3 The Interpretation of the Likelihood Ratio

8.1.4 Probabilistic Genotyping

8.1.5 The Impact of the Quality of the Model

8.2 The Concept of a Contributor

8.3 Analogies Between Mixtures and Kinship Evaluations

8.3.1 Uncertainty About Genotypes

8.3.2 Modeling Requirements

8.3.3 (In)dependence of Loci and (A)symmetry of Likelihood Ratio Distributions

8.3.4 Mixture Equivalents of the Kinship Properties

8.4 Models for Mixture Likelihoods

8.4.1 No Model: Ignore Mixtures

8.4.2 Inclusion/Exclusion Probabilities

8.4.3 Likelihood Ratios Based on Matching Profiles

8.4.4 Discrete Versus Continuous Models

8.5 The Top-down Approach

8.5.1 The Top-down Likelihood Ratio

8.5.2 Examples of the Top-down Approach

8.5.3 Heuristics and Further Discussion of the Top-down Approach

8.6 Maximum Likelihood Versus Integration

8.6.1 The Profiles of the Unknown Contributors as Model Parameters

8.7 Summary and Conclusions

8.8 Bibliographical Notes

9 p-Values of Likelihood Ratios

9.1 p-Values of Likelihood Ratios

9.2 p-Values May Change if the Distribution of Unobserved Possibilities Changes

9.3 p-Values are Ambiguous

9.4 p-Values May Appear to Support the Wrong Hypothesis

9.5 Error Rates and the Prosecutor's Fallacy

9.6 Consequences for Casework

9.6.1 Unusually Strong or Weak Evidence

9.6.2 Rates of Misleading Evidence

9.6.3 No Additional Evidence Found.

9.7 More Problems with Evidential Interpretations of p-Values

9.7.1 Multiple Peeks at Data

9.7.2 Manipulating p-Values?

9.7.3 Multiple Hypotheses

9.7.4 The Illogic of p-Value Procedures

9.8 Summary and Conclusions

9.9 Bibliographical Notes

10 From Evidence to Decision

10.1 Neyman-Pearson Theory

10.1.1 Example: Kinship Likelihood Ratios on a Single Locus

10.1.2 Composite Hypotheses and Nuisance Parameters

10.1.3 The Evidential Value of a Decision

10.1.4 Is a Decision Correct?

10.2 Applications

10.3 Bayesian Decision Theory

10.4 Evidence and Decision in a Legal Context

10.5 Summary and Conclusions

10.6 Bibliographical Notes

11 The Interpretation of DNA Database Matches

11.1 The Database Controversy

11.2 Mathematical Modeling and the Basic Formula

11.3 Evaluation of the Probabilities in Particular Cases

11.3.1 Cold Case Search

11.3.2 Targeted Search

11.3.3 Probable Cause

11.3.4 Casework

11.3.5 The Multi-stain Problem

11.4 Which Likelihood Ratio?

11.4.1 Cold Case Search

11.4.2 Targeted Search

11.5 Only a Unique Match is Known

11.6 An Intermediate Situation

11.7 A Further Analysis of the Controversies

11.7.1 Against 1/(np): A Large Database Should Give Strong Evidence

11.7.2 Against 1/(np): Growing Database

11.7.3 Matches in a Larger Database are not Necessarily More Likely to be With the Trace Donor

11.7.4 Against 1/(np): Cunning Defense Lawyer

11.7.5 Against 1/p: Data-Driven Hypotheses

11.7.6 Relevance of (Offender) Population Size

11.7.7 Inadmissibility of Hypotheses About C ∈ D

11.7.8 A Frequentist Interpretation

11.8 Analogies with Example 2.2.1

11.9 Summary and Conclusions

11.10 Bibliographical Notes

12 Familial Searching

12.1 Probabilistic Assessments for Familial Searching

12.2 Search Strategies.

12.2.1 Strategy Properties

12.3 Strategy Performance

12.3.1 The Top-k Strategy

12.3.2 Comparison of the LR-threshold and Threshold Top-k Strategies With the Top-k Strategy

12.4 Search Strategies and the Neyman-Pearson Lemma

12.5 Summary and Conclusions

12.6 Bibliographical Notes

13 Belief Functions and their Applications

13.1 The Basics of Belief Functions

13.2 Conditional Belief

13.3 The Island Problems with Belief Functions

13.3.1 The Classical Case

13.3.2 The Search Case

13.4 Parental Identification

13.4.1 Paternal Allele Known

13.4.2 Paternal Allele Not Known

13.4.3 Multiple Loci

13.5 Finding Persons with Special Features

13.6 The Legal Practice with Belief Functions

13.7 A Philosophical Back-up of Belief Functions

13.8 Summary and Conclusions

13.9 Bibliographical Notes

14 Recommendation Reports

14.1 ENFSI Guideline for Evaluative Reporting in Forensic Science

14.2 The PCAST Report to the President

14.3 Twelve Guiding Principles and Recommendations

14.4 DNA Commission of the International Society for Forensic Genetics

14.5 The SWGDAM Interpretation Guidelines

14.6 A Guideline for Validation

14.7 Summary and Conclusions

14.8 Bibliographical Notes

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 09 Apr 2021).

ISBN:

1-108-69247-8

1-108-68971-X

1-108-59617-7

OCLC:

1295277933