Contents:

Summary: 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..
Intro -- Statistical Analysis in Forensic Science -- Contents -- Preface -- 1 Physicochemical data obtained in forensic science laboratories -- 1.1 Introduction -- 1.2 Glass -- 1.2.1 SEM-EDX technique -- 1.2.2 GRIM technique -- 1.3 Flammable liquids: ATD-GC/MS technique -- 1.4 Car paints: Py-GC/MS technique -- 1.5 Fibres and inks: MSP-DAD technique -- References -- 2 Evaluation of evidence in the form of physicochemical data -- 2.1 Introduction -- 2.2 Comparison problem -- 2.2.1 Two-stage approach -- 2.2.2 Likelihood ratio approach -- 2.2.3 Difference between an application of two-stage approach and likelihood ratio approach -- 2.3 Classification problem -- 2.3.1 Chemometric approach -- 2.3.2 Likelihood ratio approach -- 2.4 Likelihood ratio and Bayes' theorem -- References -- 3 Continuous data -- 3.1 Introduction -- 3.2 Data transformations -- 3.3 Descriptive statistics -- 3.3.1 Measures of location -- 3.3.2 Dispersion: Variance estimation -- 3.3.3 Data distribution -- 3.3.4 Correlation -- 3.3.5 Continuous probability distributions -- 3.4 Hypothesis testing -- 3.4.1 Introduction -- 3.4.2 Hypothesis test for a population mean for samples with known variance from a normal distribution -- 3.4.3 Hypothesis test for a population mean for small samples with unknown variance from a normal distribution -- 3.4.4 Relation between tests and confidence intervals -- 3.4.5 Hypothesis test based on small samples for a difference in the means of two independent populations with unknown variances from normal distributions -- 3.4.6 Paired comparisons -- 3.4.7 Hotelling's test -- 3.4.8 Significance test for correlation coefficient -- 3.5 Analysis of variance -- 3.5.1 Principles of ANOVA -- 3.5.2 Feature selection with application of ANOVA -- 3.5.3 Testing of the equality of variances -- 3.6 Cluster analysis -- 3.6.1 Similarity measurements.

3.6.2 Hierarchical cluster analysis -- 3.7 Dimensionality reduction -- 3.7.1 Principal component analysis -- 3.7.2 Graphical models -- References -- 4 Likelihood ratio models for comparison problems -- 4.1 Introduction -- 4.2 Normal between-object distribution -- 4.2.1 Multivariate data -- 4.2.2 Univariate data -- 4.3 Between-object distribution modelled by kernel density estimation -- 4.3.1 Multivariate data -- 4.3.2 Univariate data -- 4.4 Examples -- 4.4.1 Univariate research data - normal between-object distribution - R software -- 4.4.2 Univariate casework data - normal between-object distribution - Bayesian network -- 4.4.3 Univariate research data - kernel density estimation - R software -- 4.4.4 Univariate casework data - kernel density estimation - calcuLatoR software -- 4.4.5 Multivariate research data - normal between-object distribution - R software -- 4.4.6 Multivariate research data - kernel density estimation procedure - R software -- 4.4.7 Multivariate casework data - kernel density estimation - R software -- 4.5 R Software -- 4.5.1 Routines for casework applications -- 4.5.2 Routines for research applications -- References -- 5 Likelihood ratio models for classification problems -- 5.1 Introduction -- 5.2 Normal between-object distribution -- 5.2.1 Multivariate data -- 5.2.2 Univariate data -- 5.2.3 One-level models -- 5.3 Between-object distribution modelled by kernel density estimation -- 5.3.1 Multivariate data -- 5.3.2 Univariate data -- 5.3.3 One-level models -- 5.4 Examples -- 5.4.1 Univariate casework data - normal between-object distribution - Bayesian network -- 5.4.2 Univariate research data - kernel density estimation procedure - R software -- 5.4.3 Multivariate research data - kernel density estimation - R software -- 5.4.4 Multivariate casework data - kernel density estimation - R software -- 5.5 R software.

5.5.1 Routines for casework applications -- 5.5.2 Routines for research applications -- References -- 6 Performance of likelihood ratio methods -- 6.1 Introduction -- 6.2 Empirical measurement of the performance of likelihood ratios -- 6.3 Histograms and Tippett plots -- 6.4 Measuring discriminating power -- 6.4.1 False positive and false negative rates -- 6.4.2 Discriminating power: A definition -- 6.4.3 Measuring discriminating power with DET curves -- 6.4.4 Is discriminating power enough? -- 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots -- 6.5.1 Accuracy in a classical example: Weather forecasting -- 6.5.2 Calibration -- 6.5.3 Adaptation to forensic inference using likelihood ratios -- 6.6 Comparison of the performance of different methods for LR computation -- 6.6.1 MSP-DAD data from comparison of inks -- 6.6.2 Py-GC/MS data from comparison of car paints -- 6.6.3 SEM-EDX data for classification of glass objects -- 6.7 Conclusions: What to measure, and how -- 6.8 Software -- References -- Appendix A Probability -- A.1 Laws of probability -- A.2 Bayes' theorem and the likelihood ratio -- A.3 Probability distributions for discrete data -- A.4 Probability distributions for continuous data -- References -- Appendix B Matrices: An introduction tomatrix algebra -- B.1 Multiplication by a constant -- B.2 Adding matrices -- B.3 Multiplying matrices -- B.4 Matrix transposition -- B.5 Determinant of a matrix -- B.6 Matrix inversion -- B.7 Matrix equations -- B.8 Eigenvectors and eigenvalues -- Reference -- Appendix C Pool adjacent violators algorithm -- References -- Appendix D Introduction to R software -- D.1 Becoming familiar with R -- D.2 Basic mathematical operations in R -- D.2.1 Vector algebra -- D.2.2 Matrix algebra -- D.3 Data input -- D.4 Functions in R -- D.5 Dereferencing.

D.6 Basic statistical functions -- D.7 Graphics with R -- D.7.1 Box-plots -- D.7.2 Q-Q plots -- D.7.3 Normal distribution -- D.7.4 Histograms -- D.7.5 Kernel density estimation -- D.7.6 Correlation between variables -- D.8 Saving data -- D.9 R codes used in Chapters 4 and 5 -- D.9.1 Comparison problems in casework studies -- D.9.2 Comparison problems in research studies -- D.9.3 Classification problems in casework studies -- D.9.4 Classification problems in research studies -- D.10 Evaluating the performance of LR models -- D.10.1 Histograms -- D.10.2 Tippett plots -- D.10.3 DET plots -- D.10.4 ECE plots -- Reference -- Appendix E Bayesian network models -- E.1 Introduction to Bayesian networks -- E.2 Introduction to Hugin Researcher™ software -- E.2.1 Basic functions -- E.2.2 Creating a new Bayesian network -- E.2.3 Calculations -- References -- Appendix F Introduction to calcuLatoR software -- F.1 Introduction -- F.2 Manual -- Reference -- Index.

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Intro -- Statistical Analysis in Forensic Science -- Contents -- Preface -- 1 Physicochemical data obtained in forensic science laboratories -- 1.1 Introduction -- 1.2 Glass -- 1.2.1 SEM-EDX technique -- 1.2.2 GRIM technique -- 1.3 Flammable liquids: ATD-GC/MS technique -- 1.4 Car paints: Py-GC/MS technique -- 1.5 Fibres and inks: MSP-DAD technique -- References -- 2 Evaluation of evidence in the form of physicochemical data -- 2.1 Introduction -- 2.2 Comparison problem -- 2.2.1 Two-stage approach -- 2.2.2 Likelihood ratio approach -- 2.2.3 Difference between an application of two-stage approach and likelihood ratio approach -- 2.3 Classification problem -- 2.3.1 Chemometric approach -- 2.3.2 Likelihood ratio approach -- 2.4 Likelihood ratio and Bayes' theorem -- References -- 3 Continuous data -- 3.1 Introduction -- 3.2 Data transformations -- 3.3 Descriptive statistics -- 3.3.1 Measures of location -- 3.3.2 Dispersion: Variance estimation -- 3.3.3 Data distribution -- 3.3.4 Correlation -- 3.3.5 Continuous probability distributions -- 3.4 Hypothesis testing -- 3.4.1 Introduction -- 3.4.2 Hypothesis test for a population mean for samples with known variance from a normal distribution -- 3.4.3 Hypothesis test for a population mean for small samples with unknown variance from a normal distribution -- 3.4.4 Relation between tests and confidence intervals -- 3.4.5 Hypothesis test based on small samples for a difference in the means of two independent populations with unknown variances from normal distributions -- 3.4.6 Paired comparisons -- 3.4.7 Hotelling's test -- 3.4.8 Significance test for correlation coefficient -- 3.5 Analysis of variance -- 3.5.1 Principles of ANOVA -- 3.5.2 Feature selection with application of ANOVA -- 3.5.3 Testing of the equality of variances -- 3.6 Cluster analysis -- 3.6.1 Similarity measurements.

3.6.2 Hierarchical cluster analysis -- 3.7 Dimensionality reduction -- 3.7.1 Principal component analysis -- 3.7.2 Graphical models -- References -- 4 Likelihood ratio models for comparison problems -- 4.1 Introduction -- 4.2 Normal between-object distribution -- 4.2.1 Multivariate data -- 4.2.2 Univariate data -- 4.3 Between-object distribution modelled by kernel density estimation -- 4.3.1 Multivariate data -- 4.3.2 Univariate data -- 4.4 Examples -- 4.4.1 Univariate research data - normal between-object distribution - R software -- 4.4.2 Univariate casework data - normal between-object distribution - Bayesian network -- 4.4.3 Univariate research data - kernel density estimation - R software -- 4.4.4 Univariate casework data - kernel density estimation - calcuLatoR software -- 4.4.5 Multivariate research data - normal between-object distribution - R software -- 4.4.6 Multivariate research data - kernel density estimation procedure - R software -- 4.4.7 Multivariate casework data - kernel density estimation - R software -- 4.5 R Software -- 4.5.1 Routines for casework applications -- 4.5.2 Routines for research applications -- References -- 5 Likelihood ratio models for classification problems -- 5.1 Introduction -- 5.2 Normal between-object distribution -- 5.2.1 Multivariate data -- 5.2.2 Univariate data -- 5.2.3 One-level models -- 5.3 Between-object distribution modelled by kernel density estimation -- 5.3.1 Multivariate data -- 5.3.2 Univariate data -- 5.3.3 One-level models -- 5.4 Examples -- 5.4.1 Univariate casework data - normal between-object distribution - Bayesian network -- 5.4.2 Univariate research data - kernel density estimation procedure - R software -- 5.4.3 Multivariate research data - kernel density estimation - R software -- 5.4.4 Multivariate casework data - kernel density estimation - R software -- 5.5 R software.

5.5.1 Routines for casework applications -- 5.5.2 Routines for research applications -- References -- 6 Performance of likelihood ratio methods -- 6.1 Introduction -- 6.2 Empirical measurement of the performance of likelihood ratios -- 6.3 Histograms and Tippett plots -- 6.4 Measuring discriminating power -- 6.4.1 False positive and false negative rates -- 6.4.2 Discriminating power: A definition -- 6.4.3 Measuring discriminating power with DET curves -- 6.4.4 Is discriminating power enough? -- 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots -- 6.5.1 Accuracy in a classical example: Weather forecasting -- 6.5.2 Calibration -- 6.5.3 Adaptation to forensic inference using likelihood ratios -- 6.6 Comparison of the performance of different methods for LR computation -- 6.6.1 MSP-DAD data from comparison of inks -- 6.6.2 Py-GC/MS data from comparison of car paints -- 6.6.3 SEM-EDX data for classification of glass objects -- 6.7 Conclusions: What to measure, and how -- 6.8 Software -- References -- Appendix A Probability -- A.1 Laws of probability -- A.2 Bayes' theorem and the likelihood ratio -- A.3 Probability distributions for discrete data -- A.4 Probability distributions for continuous data -- References -- Appendix B Matrices: An introduction tomatrix algebra -- B.1 Multiplication by a constant -- B.2 Adding matrices -- B.3 Multiplying matrices -- B.4 Matrix transposition -- B.5 Determinant of a matrix -- B.6 Matrix inversion -- B.7 Matrix equations -- B.8 Eigenvectors and eigenvalues -- Reference -- Appendix C Pool adjacent violators algorithm -- References -- Appendix D Introduction to R software -- D.1 Becoming familiar with R -- D.2 Basic mathematical operations in R -- D.2.1 Vector algebra -- D.2.2 Matrix algebra -- D.3 Data input -- D.4 Functions in R -- D.5 Dereferencing.

D.6 Basic statistical functions -- D.7 Graphics with R -- D.7.1 Box-plots -- D.7.2 Q-Q plots -- D.7.3 Normal distribution -- D.7.4 Histograms -- D.7.5 Kernel density estimation -- D.7.6 Correlation between variables -- D.8 Saving data -- D.9 R codes used in Chapters 4 and 5 -- D.9.1 Comparison problems in casework studies -- D.9.2 Comparison problems in research studies -- D.9.3 Classification problems in casework studies -- D.9.4 Classification problems in research studies -- D.10 Evaluating the performance of LR models -- D.10.1 Histograms -- D.10.2 Tippett plots -- D.10.3 DET plots -- D.10.4 ECE plots -- Reference -- Appendix E Bayesian network models -- E.1 Introduction to Bayesian networks -- E.2 Introduction to Hugin Researcher™ software -- E.2.1 Basic functions -- E.2.2 Creating a new Bayesian network -- E.2.3 Calculations -- References -- Appendix F Introduction to calcuLatoR software -- F.1 Introduction -- F.2 Manual -- Reference -- Index.

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..

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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