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Statistical Analysis in Forensic Science: Evidential Values of Multivariate Physicochemical Data

Book Description

A practical guide for determining the evidential value of physicochemical data

Microtraces of various materials (e.g. glass, paint, fibres, and petroleum products) are routinely subjected to physicochemical examination by forensic experts, whose role is to evaluate such physicochemical data in the context of the prosecution and defence propositions. Such examinations return various kinds of information, including quantitative data. From the forensic point of view, the most suitable way to evaluate evidence is the likelihood ratio. This book provides a collection of recent approaches to the determination of likelihood ratios and describes suitable software, with documentation and examples of their use in practice. The statistical computing and graphics software environment R, pre-computed Bayesian networks using Hugin Researcher and a new package, calcuLatoR, for the computation of likelihood ratios are all explored.

Statistical Analysis in Forensic Science will provide an invaluable practical guide for forensic experts and practitioners, forensic statisticians, analytical chemists, and chemometricians.

Key features include:

  • Description of the physicochemical analysis of forensic trace evidence.

  • Detailed description of likelihood ratio models for determining the evidential value of multivariate physicochemical data.

  • Detailed description of methods, such as empirical cross-entropy plots, for assessing the performance of likelihood ratio-based methods for evidence evaluation.

  • Routines written using the open-source R software, as well as Hugin Researcher and calcuLatoR.

  • Practical examples and recommendations for the use of all these methods in practice.

  • Table of Contents

    1. Cover
    2. Title Page
    3. Copyright
    4. Dedication
    5. Preface
    6. 1: Physicochemical data obtained in forensic science laboratories
      1. 1.1 Introduction
      2. 1.2 Glass
      3. 1.3 Flammable liquids: ATD-GC/MS technique
      4. 1.4 Car paints: Py-GC/MS technique
      5. 1.5 Fibres and inks: MSP-DAD technique
      6. References
    7. 2: Evaluation of evidence in the form of physicochemical data
      1. 2.1 Introduction
      2. 2.2 Comparison problem
      3. 2.3 Classification problem
      4. 2.4 Likelihood ratio and Bayes’ theorem
      5. References
    8. 3: Continuous data
      1. 3.1 Introduction
      2. 3.2 Data transformations
      3. 3.3 Descriptive statistics
      4. 3.4 Hypothesis testing
      5. 3.5 Analysis of variance
      6. 3.6 Cluster analysis
      7. 3.7 Dimensionality reduction
      8. References
    9. 4: Likelihood ratio models for comparison problems
      1. 4.1 Introduction
      2. 4.2 Normal between-object distribution
      3. 4.3 Between-object distribution modelled by kernel density estimation
      4. 4.4 Examples
      5. 4.5 R Software
      6. References
    10. 5: Likelihood ratio models for classification problems
      1. 5.1 Introduction
      2. 5.2 Normal between-object distribution
      3. 5.3 Between-object distribution modelled by kernel density estimation
      4. 5.4 Examples
      5. 5.5 R software
      6. References
    11. 6: Performance of likelihood ratio methods
      1. 6.1 Introduction
      2. 6.2 Empirical measurement of the performance of likelihood ratios
      3. 6.3 Histograms and Tippett plots
      4. 6.4 Measuring discriminating power
      5. 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots
      6. 6.6 Comparison of the performance of different methods for LR computation
      7. 6.7 Conclusions: What to measure, and how
      8. 6.8 Software
      9. References
    12. Appendix A: Probability
      1. A.1 Laws of probability
      2. A.2 Bayes’ theorem and the likelihood ratio
      3. A.3 Probability distributions for discrete data
      4. A.4 Probability distributions for continuous data
      5. References
    13. Appendix B: Matrices: An introduction to matrix algebra
      1. B.1 Multiplication by a constant
      2. B.2 Adding matrices
      3. B.3 Multiplying matrices
      4. B.4 Matrix transposition
      5. B.5 Determinant of a matrix
      6. B.6 Matrix inversion
      7. B.7 Matrix equations
      8. B.8 Eigenvectors and eigenvalues
      9. References
    14. Appendix C: Pool adjacent violators algorithm
      1. References
    15. Appendix D: Introduction to R software
      1. D.1 Becoming familiar with R
      2. D.2 Basic mathematical operations in R
      3. D.3 Data input
      4. D.4 Functions in R
      5. D.5 Dereferencing
      6. D.6 Basic statistical functions
      7. D.7 Graphics with R
      8. D.8 Saving data
      9. D.9 R codes used in Chapters 4 and 5
      10. D.10 Evaluating the performance of LR models
      11. Reference
    16. Appendix E: Bayesian network models
      1. E.1 Introduction to Bayesian networks
      2. E.2 Introduction to Hugin Researcher™ software
      3. References
    17. Appendix F: Introduction to calcuLatoR software
      1. F.1 Introduction
      2. F.2 Manual
      3. Reference
    18. Index