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Statistics and the Evaluation of Evidence for Forensic Scientists.

By: Contributor(s): Material type: TextTextSeries: Statistics in Practice SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2020Copyright date: ©2019Edition: 3rd edDescription: 1 online resource (1251 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119245254
Subject(s): Genre/Form: Additional physical formats: Print version:: Statistics and the Evaluation of Evidence for Forensic ScientistsDDC classification:
  • 363.23/01/5195
LOC classification:
  • HV8073 .A385 2020
Online resources:
Contents:
Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface to Third Edition -- Preface to Second Edition -- Preface to First Edition -- Chapter 1 Uncertainty in Forensic Science -- 1.1 Introduction -- 1.2 Statistics and the Law -- 1.3 Uncertainty in Scientific Evidence -- 1.3.1 The Frequentist Method -- 1.3.2 Stains of Body Fluids -- 1.3.3 Glass Fragments -- 1.4 Terminology -- 1.5 Types of Data -- 1.6 Populations -- 1.7 Probability -- 1.7.1 Introduction -- 1.7.2 A Standard for Uncertainty -- 1.7.3 Events -- 1.7.4 Classical and Frequentist Definitions of Probability and Their Limitations -- 1.7.5 Subjective Definition of Probability -- 1.7.6 The Quantification of Probability Through a Betting Scheme -- 1.7.7 Probabilities and Frequencies: The Role of Exchangeability -- 1.7.8 Laws of Probability -- 1.7.9 Dependent Events and Background Information -- 1.7.10 Law of Total Probability -- 1.7.11 Updating of Probabilities -- Chapter 2 The Evaluation of Evidence -- 2.1 Odds -- 2.1.1 Complementary Events -- 2.1.2 Examples -- 2.1.3 Definition of Odds -- 2.2 Bayes' Theorem -- 2.2.1 Statement of the Theorem -- 2.2.2 Examples -- 2.3 The Odds Form of Bayes' Theorem -- 2.3.1 Likelihood Ratio -- 2.3.2 Bayes' Factor and Likelihood Ratio -- 2.3.3 Three‐Way Tables -- 2.3.4 Logarithm of the Likelihood Ratio -- 2.4 The Value of Evidence -- 2.4.1 Evaluation of Forensic Evidence -- 2.4.2 Justification of the Use of the Likelihood Ratio -- 2.4.3 Single Value for the Likelihood Ratio -- 2.4.4 Role of Background Information -- 2.4.5 Summary of Competing Propositions -- 2.4.6 Qualitative Scale for the Value of the Evidence -- 2.5 Errors in Interpretation -- 2.5.1 Fallacy of the Transposed Conditional -- 2.5.2 Source Probability Error -- 2.5.3 Ultimate Issue Error -- 2.5.4 Defence Attorney's Fallacy -- 2.5.5 Probability (Another Match) Error.
2.5.6 Numerical Conversion Error -- 2.5.7 False Positive Fallacy -- 2.5.8 Expected Value Fallacy -- 2.5.9 Uniqueness -- 2.5.10 Other Difficulties -- 2.5.11 Empirical Evidence of Errors in Interpretation -- 2.6 Misinterpretations -- 2.7 Explanation of Transposed Conditional, Defence Attorney's and False Positive Fallacies -- 2.7.1 Explanation of the Fallacy of the Transposed Conditional -- 2.7.2 Explanation of the Defence Attorney's Fallacy -- 2.7.3 Explanation of the False Positive Fallacy -- 2.8 Making Coherent Decisions -- 2.8.1 Elements of Statistical Decision Theory -- 2.8.2 Decision Analysis: An Example -- 2.9 Graphical Probabilistic Models: Bayesian Networks -- 2.9.1 Elements of the Bayesian Networks -- 2.9.2 The Construction of Bayesian Networks -- 2.9.3 Bayesian Decision Networks (Influence Diagrams) -- Chapter 3 Historical Review -- 3.1 Early History -- 3.2 The Dreyfus Case -- 3.3 Statistical Arguments by Early Twentieth‐Century Forensic Scientists -- 3.4 People v. Collins -- 3.5 Discriminating Power -- 3.5.1 Derivation -- 3.5.2 Evaluation of Evidence by Discriminating Power -- 3.5.3 Finite Samples -- 3.5.4 Combination of Independent Systems -- 3.5.5 Correlated Attributes -- 3.6 Significance Probabilities -- 3.6.1 Calculation of Significance Probabilities -- 3.6.2 Relationship to Likelihood Ratio -- 3.6.3 Combination of Significance Probabilities -- 3.7 Coincidence Probabilities -- 3.7.1 Introduction -- 3.7.2 Comparison Stage -- 3.7.3 Significance Stage -- 3.8 Likelihood Ratio -- Chapter 4 Bayesian Inference -- 4.1 Introduction -- 4.2 Inference for a Proportion -- 4.2.1 Interval Estimation -- 4.2.2 Estimation with Zero Occurrences in a Sample -- 4.2.3 Uncertainty on Sensitivity and Specificity -- 4.3 Sampling -- 4.3.1 Choice of Sample Size in Large Consignments -- 4.3.2 Choice of Sample Size in Small Consignments.
4.4 Bayesian Networks for Sampling Inspection -- 4.4.1 Large Consignments -- 4.4.2 Small Consignments -- 4.5 Inference for a Normal Mean -- 4.5.1 Known Variance -- 4.5.2 Unknown Variance -- 4.5.3 Interval Estimation -- 4.6 Quantity Estimation -- 4.6.1 Predictive Approach in Small Consignments -- 4.6.2 Predictive Approach in Large Consignments -- 4.7 Decision Analysis -- 4.7.1 Standard Loss Functions -- 4.7.2 Decision Analysis for Forensic Sampling -- Chapter 5 Evidence and Propositions: Theory -- 5.1 The Choice of Propositions and Pre‐Assessment -- 5.2 Levels of Propositions and Roles of the Forensic Scientist -- 5.3 The Formal Development of a Likelihood Ratio for Different Propositions and Discrete Characteristics -- 5.3.1 Likelihood Ratio with Source Level Propositions -- 5.3.2 Likelihood Ratio with Activity Level Propositions -- 5.3.3 Likelihood Ratio with Offence Level Propositions -- 5.4 Validation of Bayesian Network Structures: An Example -- 5.5 Pre‐Assessment -- 5.5.1 Pre‐assessment of the Case -- 5.5.2 Pre‐assessment of Evidence -- 5.5.3 Pre‐assessment: A Practical Example -- 5.6 Combination of Items of Evidence -- 5.6.1 A Difficulty in Combining Evidence: The Problem of Conjunction -- 5.6.2 Generic Patterns of Inference in Combining Evidence -- Chapter 6 Evidence and Propositions: Practice -- 6.1 Examples for Evaluation given Source Level Propositions -- 6.1.1 General Population -- 6.1.2 Particular Population -- 6.1.3 A Note on The Appropriate Databases for Evaluation Given Source Level Propositions -- 6.1.4 Two Trace Problem -- 6.1.5 Many Samples -- 6.1.6 Multiple Propositions -- 6.1.7 A Note on Biological Traces -- 6.1.8 Additional Considerations on Source Level Propositions -- 6.2 Examples for Evaluation given Activity Level Propositions -- 6.2.1 A Practical Approach to Fibres Evaluation -- 6.2.2 A Practical Approach to Glass Evaluation.
6.2.3 The Assignment of Probabilities for Transfer Events -- 6.2.4 The Assignment of Probabilities for Background Traces -- 6.2.5 Presence of Material with Non‐corresponding Features -- 6.2.6 Absence of Evidence for Activity Level Propositions -- 6.3 Examples for Evaluation given Offence Level Propositions -- 6.3.1 One Stain, k Offenders -- 6.3.2 Two Stains, One Offender -- 6.3.3 Paternity and The Combination of Likelihood Ratios -- 6.3.4 Probability of Paternity -- 6.3.5 Absence of Evidence for Offence Level Propositions -- 6.3.6 A Note on Relevance and Offence Level Propositions -- 6.4 Summary -- 6.4.1 Stain Known to Have Been Left by Offenders: Source‐Level Propositions -- 6.4.2 Material Known to Have Been (or Not to Have Been) Left by Offenders: Activity‐Level Propositions -- 6.4.3 Stain May Not Have Been Left by Offenders: Offence‐Level Propositions -- Chapter 7 Data Analysis -- 7.1 Introduction -- 7.2 Theory for Discrete Data -- 7.2.1 Data of Independent Counts with a Poisson Distribution -- 7.2.2 Data of Independent Counts with a Binomial Distribution -- 7.2.3 Data of Independent Counts with a Multinomial Distribution -- 7.3 Theory for Continuous Univariate Data -- 7.3.1 Assessment of Similarity Only -- 7.3.2 Sources of Variation: Two‐Level Models -- 7.3.3 Transfer Probability -- 7.4 Normal Between‐Source Variation -- 7.4.1 Marginal Distribution of Measurements -- 7.4.2 Approximate Derivation of the Likelihood Ratio -- 7.4.3 Lindley's Approach -- 7.4.4 Interpretation of Result -- 7.4.5 Examples -- 7.5 Non‐normal Between‐Source Variation -- 7.5.1 Estimation of a Probability Density Function -- 7.5.2 Kernel Density Estimation for Between‐Source Data -- 7.5.3 Examples -- 7.6 Multivariate Analysis -- 7.6.1 Introduction -- 7.6.2 Multivariate Two‐Level Models -- 7.6.3 A Note on Sensitivity -- 7.6.4 Case Study for Two‐Level Data.
7.6.5 Three‐Level Models -- 7.7 Discrimination -- 7.7.1 Discrete Data -- 7.7.2 Continuous Data -- 7.7.3 Autocorrelated Data -- 7.7.4 Multivariate Data -- 7.7.5 Cut‐Offs and Legal Thresholds -- 7.8 Score‐Based Models -- 7.8.1 Example -- 7.9 Bayes' Factor and Likelihood Ratio (cont.) -- Chapter 8 Assessment of the Performance of Methods for the Evaluation of Evidence -- 8.1 Introduction -- 8.2 Properties of Methods for Evaluation -- 8.3 General Topics Relating to Sample Size Estimation and to Assessment -- 8.3.1 Probability of Strong Misleading Evidence: A Sample Size Problem -- 8.3.2 Calibration -- 8.4 Assessment of Performance of a Procedure for the Calculation of the Likelihood Ratio -- 8.4.1 Histograms and Tippett Plots -- 8.4.2 False Positive Rates, False Negative Rates and DET Plots -- 8.4.3 Empirical Cross‐Entropy -- 8.5 Case Study: Kinship Analysis -- 8.6 Conclusion -- Appendix A Probability Distributions -- A.1 Introduction -- A.2 Probability Distributions for Counts -- A.2.1 Probabilities -- A.2.2 Summary Measures -- A.2.3 Binomial Distribution -- A.2.4 Multinomial Distribution -- A.2.5 Hypergeometric Distribution -- A.2.6 Poisson Distribution -- A.2.7 Beta‐Binomial and Dirichlet‐Multinomial Distributions -- A.3 Measurements -- A.3.1 Summary Statistics -- A.3.2 Normal Distribution -- A.3.3 Jeffreys' Prior Distributions -- A.3.4 Student's t‐Distribution -- A.3.5 Gamma and Chi‐Squared Distributions -- A.3.6 Inverse Gamma and Inverse Chi‐Squared Distributions -- A.3.7 Beta Distribution -- A.3.8 Dirichlet Distribution -- A.3.9 Multivariate Normal Distribution and Correlation -- A.3.10 Wishart Distribution -- A.3.11 Inverse Wishart Distribution -- Appendix B Matrix Properties -- B.1 Matrix Terminology -- B.1.1 The Trace of a Square Matrix -- B.1.2 The Transpose of a Matrix -- B.1.3 Addition of Two Matrices -- B.1.4 Determinant of a Matrix.
B.1.5 Matrix Multiplication.
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Cover -- Title Page -- Copyright -- Contents -- Foreword -- Preface to Third Edition -- Preface to Second Edition -- Preface to First Edition -- Chapter 1 Uncertainty in Forensic Science -- 1.1 Introduction -- 1.2 Statistics and the Law -- 1.3 Uncertainty in Scientific Evidence -- 1.3.1 The Frequentist Method -- 1.3.2 Stains of Body Fluids -- 1.3.3 Glass Fragments -- 1.4 Terminology -- 1.5 Types of Data -- 1.6 Populations -- 1.7 Probability -- 1.7.1 Introduction -- 1.7.2 A Standard for Uncertainty -- 1.7.3 Events -- 1.7.4 Classical and Frequentist Definitions of Probability and Their Limitations -- 1.7.5 Subjective Definition of Probability -- 1.7.6 The Quantification of Probability Through a Betting Scheme -- 1.7.7 Probabilities and Frequencies: The Role of Exchangeability -- 1.7.8 Laws of Probability -- 1.7.9 Dependent Events and Background Information -- 1.7.10 Law of Total Probability -- 1.7.11 Updating of Probabilities -- Chapter 2 The Evaluation of Evidence -- 2.1 Odds -- 2.1.1 Complementary Events -- 2.1.2 Examples -- 2.1.3 Definition of Odds -- 2.2 Bayes' Theorem -- 2.2.1 Statement of the Theorem -- 2.2.2 Examples -- 2.3 The Odds Form of Bayes' Theorem -- 2.3.1 Likelihood Ratio -- 2.3.2 Bayes' Factor and Likelihood Ratio -- 2.3.3 Three‐Way Tables -- 2.3.4 Logarithm of the Likelihood Ratio -- 2.4 The Value of Evidence -- 2.4.1 Evaluation of Forensic Evidence -- 2.4.2 Justification of the Use of the Likelihood Ratio -- 2.4.3 Single Value for the Likelihood Ratio -- 2.4.4 Role of Background Information -- 2.4.5 Summary of Competing Propositions -- 2.4.6 Qualitative Scale for the Value of the Evidence -- 2.5 Errors in Interpretation -- 2.5.1 Fallacy of the Transposed Conditional -- 2.5.2 Source Probability Error -- 2.5.3 Ultimate Issue Error -- 2.5.4 Defence Attorney's Fallacy -- 2.5.5 Probability (Another Match) Error.

2.5.6 Numerical Conversion Error -- 2.5.7 False Positive Fallacy -- 2.5.8 Expected Value Fallacy -- 2.5.9 Uniqueness -- 2.5.10 Other Difficulties -- 2.5.11 Empirical Evidence of Errors in Interpretation -- 2.6 Misinterpretations -- 2.7 Explanation of Transposed Conditional, Defence Attorney's and False Positive Fallacies -- 2.7.1 Explanation of the Fallacy of the Transposed Conditional -- 2.7.2 Explanation of the Defence Attorney's Fallacy -- 2.7.3 Explanation of the False Positive Fallacy -- 2.8 Making Coherent Decisions -- 2.8.1 Elements of Statistical Decision Theory -- 2.8.2 Decision Analysis: An Example -- 2.9 Graphical Probabilistic Models: Bayesian Networks -- 2.9.1 Elements of the Bayesian Networks -- 2.9.2 The Construction of Bayesian Networks -- 2.9.3 Bayesian Decision Networks (Influence Diagrams) -- Chapter 3 Historical Review -- 3.1 Early History -- 3.2 The Dreyfus Case -- 3.3 Statistical Arguments by Early Twentieth‐Century Forensic Scientists -- 3.4 People v. Collins -- 3.5 Discriminating Power -- 3.5.1 Derivation -- 3.5.2 Evaluation of Evidence by Discriminating Power -- 3.5.3 Finite Samples -- 3.5.4 Combination of Independent Systems -- 3.5.5 Correlated Attributes -- 3.6 Significance Probabilities -- 3.6.1 Calculation of Significance Probabilities -- 3.6.2 Relationship to Likelihood Ratio -- 3.6.3 Combination of Significance Probabilities -- 3.7 Coincidence Probabilities -- 3.7.1 Introduction -- 3.7.2 Comparison Stage -- 3.7.3 Significance Stage -- 3.8 Likelihood Ratio -- Chapter 4 Bayesian Inference -- 4.1 Introduction -- 4.2 Inference for a Proportion -- 4.2.1 Interval Estimation -- 4.2.2 Estimation with Zero Occurrences in a Sample -- 4.2.3 Uncertainty on Sensitivity and Specificity -- 4.3 Sampling -- 4.3.1 Choice of Sample Size in Large Consignments -- 4.3.2 Choice of Sample Size in Small Consignments.

4.4 Bayesian Networks for Sampling Inspection -- 4.4.1 Large Consignments -- 4.4.2 Small Consignments -- 4.5 Inference for a Normal Mean -- 4.5.1 Known Variance -- 4.5.2 Unknown Variance -- 4.5.3 Interval Estimation -- 4.6 Quantity Estimation -- 4.6.1 Predictive Approach in Small Consignments -- 4.6.2 Predictive Approach in Large Consignments -- 4.7 Decision Analysis -- 4.7.1 Standard Loss Functions -- 4.7.2 Decision Analysis for Forensic Sampling -- Chapter 5 Evidence and Propositions: Theory -- 5.1 The Choice of Propositions and Pre‐Assessment -- 5.2 Levels of Propositions and Roles of the Forensic Scientist -- 5.3 The Formal Development of a Likelihood Ratio for Different Propositions and Discrete Characteristics -- 5.3.1 Likelihood Ratio with Source Level Propositions -- 5.3.2 Likelihood Ratio with Activity Level Propositions -- 5.3.3 Likelihood Ratio with Offence Level Propositions -- 5.4 Validation of Bayesian Network Structures: An Example -- 5.5 Pre‐Assessment -- 5.5.1 Pre‐assessment of the Case -- 5.5.2 Pre‐assessment of Evidence -- 5.5.3 Pre‐assessment: A Practical Example -- 5.6 Combination of Items of Evidence -- 5.6.1 A Difficulty in Combining Evidence: The Problem of Conjunction -- 5.6.2 Generic Patterns of Inference in Combining Evidence -- Chapter 6 Evidence and Propositions: Practice -- 6.1 Examples for Evaluation given Source Level Propositions -- 6.1.1 General Population -- 6.1.2 Particular Population -- 6.1.3 A Note on The Appropriate Databases for Evaluation Given Source Level Propositions -- 6.1.4 Two Trace Problem -- 6.1.5 Many Samples -- 6.1.6 Multiple Propositions -- 6.1.7 A Note on Biological Traces -- 6.1.8 Additional Considerations on Source Level Propositions -- 6.2 Examples for Evaluation given Activity Level Propositions -- 6.2.1 A Practical Approach to Fibres Evaluation -- 6.2.2 A Practical Approach to Glass Evaluation.

6.2.3 The Assignment of Probabilities for Transfer Events -- 6.2.4 The Assignment of Probabilities for Background Traces -- 6.2.5 Presence of Material with Non‐corresponding Features -- 6.2.6 Absence of Evidence for Activity Level Propositions -- 6.3 Examples for Evaluation given Offence Level Propositions -- 6.3.1 One Stain, k Offenders -- 6.3.2 Two Stains, One Offender -- 6.3.3 Paternity and The Combination of Likelihood Ratios -- 6.3.4 Probability of Paternity -- 6.3.5 Absence of Evidence for Offence Level Propositions -- 6.3.6 A Note on Relevance and Offence Level Propositions -- 6.4 Summary -- 6.4.1 Stain Known to Have Been Left by Offenders: Source‐Level Propositions -- 6.4.2 Material Known to Have Been (or Not to Have Been) Left by Offenders: Activity‐Level Propositions -- 6.4.3 Stain May Not Have Been Left by Offenders: Offence‐Level Propositions -- Chapter 7 Data Analysis -- 7.1 Introduction -- 7.2 Theory for Discrete Data -- 7.2.1 Data of Independent Counts with a Poisson Distribution -- 7.2.2 Data of Independent Counts with a Binomial Distribution -- 7.2.3 Data of Independent Counts with a Multinomial Distribution -- 7.3 Theory for Continuous Univariate Data -- 7.3.1 Assessment of Similarity Only -- 7.3.2 Sources of Variation: Two‐Level Models -- 7.3.3 Transfer Probability -- 7.4 Normal Between‐Source Variation -- 7.4.1 Marginal Distribution of Measurements -- 7.4.2 Approximate Derivation of the Likelihood Ratio -- 7.4.3 Lindley's Approach -- 7.4.4 Interpretation of Result -- 7.4.5 Examples -- 7.5 Non‐normal Between‐Source Variation -- 7.5.1 Estimation of a Probability Density Function -- 7.5.2 Kernel Density Estimation for Between‐Source Data -- 7.5.3 Examples -- 7.6 Multivariate Analysis -- 7.6.1 Introduction -- 7.6.2 Multivariate Two‐Level Models -- 7.6.3 A Note on Sensitivity -- 7.6.4 Case Study for Two‐Level Data.

7.6.5 Three‐Level Models -- 7.7 Discrimination -- 7.7.1 Discrete Data -- 7.7.2 Continuous Data -- 7.7.3 Autocorrelated Data -- 7.7.4 Multivariate Data -- 7.7.5 Cut‐Offs and Legal Thresholds -- 7.8 Score‐Based Models -- 7.8.1 Example -- 7.9 Bayes' Factor and Likelihood Ratio (cont.) -- Chapter 8 Assessment of the Performance of Methods for the Evaluation of Evidence -- 8.1 Introduction -- 8.2 Properties of Methods for Evaluation -- 8.3 General Topics Relating to Sample Size Estimation and to Assessment -- 8.3.1 Probability of Strong Misleading Evidence: A Sample Size Problem -- 8.3.2 Calibration -- 8.4 Assessment of Performance of a Procedure for the Calculation of the Likelihood Ratio -- 8.4.1 Histograms and Tippett Plots -- 8.4.2 False Positive Rates, False Negative Rates and DET Plots -- 8.4.3 Empirical Cross‐Entropy -- 8.5 Case Study: Kinship Analysis -- 8.6 Conclusion -- Appendix A Probability Distributions -- A.1 Introduction -- A.2 Probability Distributions for Counts -- A.2.1 Probabilities -- A.2.2 Summary Measures -- A.2.3 Binomial Distribution -- A.2.4 Multinomial Distribution -- A.2.5 Hypergeometric Distribution -- A.2.6 Poisson Distribution -- A.2.7 Beta‐Binomial and Dirichlet‐Multinomial Distributions -- A.3 Measurements -- A.3.1 Summary Statistics -- A.3.2 Normal Distribution -- A.3.3 Jeffreys' Prior Distributions -- A.3.4 Student's t‐Distribution -- A.3.5 Gamma and Chi‐Squared Distributions -- A.3.6 Inverse Gamma and Inverse Chi‐Squared Distributions -- A.3.7 Beta Distribution -- A.3.8 Dirichlet Distribution -- A.3.9 Multivariate Normal Distribution and Correlation -- A.3.10 Wishart Distribution -- A.3.11 Inverse Wishart Distribution -- Appendix B Matrix Properties -- B.1 Matrix Terminology -- B.1.1 The Trace of a Square Matrix -- B.1.2 The Transpose of a Matrix -- B.1.3 Addition of Two Matrices -- B.1.4 Determinant of a Matrix.

B.1.5 Matrix Multiplication.

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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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