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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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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Seitenzahl: 456
Veröffentlichungsjahr: 2013
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Contents
Cover
Title Page
Copyright
Dedication
Preface
1: Physicochemical data obtained in forensic science laboratories
1.1 Introduction
1.2 Glass
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
2.3 Classification problem
2.4 Likelihood ratio and Bayes’ theorem
References
3: Continuous data
3.1 Introduction
3.2 Data transformations
3.3 Descriptive statistics
3.4 Hypothesis testing
3.5 Analysis of variance
3.6 Cluster analysis
3.7 Dimensionality reduction
References
4: Likelihood ratio models for comparison problems
4.1 Introduction
4.2 Normal between-object distribution
4.3 Between-object distribution modelled by kernel density estimation
4.4 Examples
4.5 R Software
References
5: Likelihood ratio models for classification problems
5.1 Introduction
5.2 Normal between-object distribution
5.3 Between-object distribution modelled by kernel density estimation
5.4 Examples
5.5 R software
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
6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots
6.6 Comparison of the performance of different methods for LR computation
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 to matrix 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
References
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.3 Data input
D.4 Functions in R
D.5 Dereferencing
D.6 Basic statistical functions
D.7 Graphics with R
D.8 Saving data
D.9 R codes used in Chapters 4 and 5
D.10 Evaluating the performance of LR models
Reference
Appendix E: Bayesian network models
E.1 Introduction to Bayesian networks
E.2 Introduction to Hugin Researcher™ software
References
Appendix F: Introduction to calcuLatoR software
F.1 Introduction
F.2 Manual
Reference
Index
This edition first published 2014 © 2014 John Wiley & Sons, Ltd
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Library of Congress Cataloging-in-Publication Data
Statistical analysis in forensic science : evidential value of multivariate physicochemical data / Grzegorz Zadora, Agnieszka Martyna, Daniel Ramos, Colin Aitken. p. cm. Includes bibliographical references and index. ISBN 978-0-470-97210-6 (cloth)1. Chemistry, Forensic. 2. Forensic statistics. 3. Chemometrics. I. Zadora, Grzegorz. II. Martyna, Agnieszka. III. Ramos, Daniel. IV. Aitken, Colin. RA1057.S73 2014 614′.12–dc232013031698
A catalogue record for this book is available from the British Library.
ISBN: 978-0-470-97210-6
To our families
Preface
An increase in the danger from new forms of crime and the need by those who administer justice for higher standards of scientific work require the development of new methods for measuring the evidential value of physicochemical data obtained during the analysis of various kinds of trace evidence.
The physicochemical analysis of various types of evidence by the application of various analytical methods (Chapter 1) returns numerous types of information including multivariate quantitative data (Chapter 3, Appendix B), for example, concentrations of elements or the refractive index of a glass fragment. The role of the forensic expert is to evaluate such physicochemical data (evidence, E) in the context of two competing propositions H1 and H2 (Chapter 2, Appendix A). The propositions H1 and H2 may be put forward by the police, prosecutors, defenders or the courts and they concern:
comparison problems (Chapter 4), for example where H1 states that the glass samples being compared originate from the same object, and H2 that the glass samples being compared originate from different objects;classification problems (Chapter 5), for example where H1 states that the glass sample which has been analysed originates from a car or building window, and H2 states that the glass sample analysed originates from a container glass.Bayesian models have been proposed for the evaluation of the evidence in such contexts. Statistical analysis is used to evaluate the evidence. The value of the evidence is determined by the likelihood ratio (LR). This is the ratio of the probability of the evidence if H1 is true, P(E | H1), to the probability of the evidence if H2 is true, P(E | H2). For evidence in the form of continuous data these probabilities are replaced with probability density functions, f(E | H1) and f(E | H2).
The LR approach (Chapter 2, Appendix A) has become increasingly popular for evidence evaluation in forensic sciences. For physicochemical data, the approach enables an objective evaluation of the physicochemical information about the analysed object(s) obtained from an analytical run, and about the rarity of the determined physicochemical features for recovered and/or control samples within a relevant population (Chapters 2, 4 and 5). The most common application of the LR approach in forensic science is in DNA profiling. The LR approach has also been applied to other evidence categories including earprints, fingerprints, firearms and toolmarks, hair, documents, envelopes and handwriting, and speaker recognition. In recent years, much has also been published on LR approaches for multivariate data. Some of these ideas (including examples from practice in forensic science) are discussed in this book.
The performance of each statistical approach should be subjected to critical analysis, not only in the form of error rates but also through the use of other formal frameworks which provide a measure of the quality of a method for the evaluation of evidence based on a likelihood ratio. There is a need not only for the measurement of the discriminating power of the LR models as represented by false positive and false negative rates, but for the information that the LR provides to the inference process in evidence evaluation, where the important concept of calibration plays a significant role. One of the objectives of this book is to consider the problem of the assessment of the performance of LR-based evidence evaluation methods. Several methods found in the literature are extensively described and compared, such as Tippett plots, detection error trade-off plots (DET) and empirical cross-entropy (ECE) plots (Chapter 6, Appendix C).
One reason for the slow implementation of these LR models is that there is a lack of commercial software to enable the calculation of the LR relatively easily by those without experience in programming (like most forensic experts). Therefore, in order to use these methods case-specific routines have to be written using an appropriate software package, such as the R software (www.r-project.org). Based on information gathered during workshops on statistics for forensic scientists (e.g. the “FORSTAT – Forensic Statistics” project under the auspices of the European Network of Forensic Sciences Institutes), the present authors believe that there is a need for a book that provides descriptions of the models in more detail than in published papers, as well as of the software routines, together with practical examples. Therefore, the aims of this book are to present and discuss recent LR approaches and to provide suitable software toolboxes with annotation and examples to illustrate the use of the approaches in practice. The routines included in the book are available from the website www.wiley.com/go/physicochemical. These include routines in R (Appendix D), pre-computed Bayesian networks for Hugin Researcher™ (Appendix E), and the calcuLatoR software (Appendix F) for the computation of likelihood ratios for univariate data. Manuals (Appendices D–F) including examples and recommendations of the use of all of these assessment methods in practice are included, as well as software and practical examples to enable forensic experts to begin to work with them immediately (Chapters 3–6).
Note also that the LR approaches presented in the book can be used whenever evidence is to be evaluated under the circumstances of two propositions. Therefore, the models described in the book can also be applied in other areas of analytical chemistry. Special emphasis is placed on the solution of problems where a decision made on the basis of results of statistical analyses of physicochemical data could have serious legal or economical consequences; thus, for example, one of these other areas of analytical chemistry could be that of food authenticity analysis.
Many people have helped in many ways in the preparation of this book, too many to enable us to acknowledge them all individually. However, we wish to acknowledge in particular Rafal Borusiewicz, Jakub M. Milczarek, David Lucy, Tereza Neocleous, Beata M. Trzcinska, and Janina Zieba-Palus for many helpful discussions and a great deal of collaborative work, from which we have been able to take much inspiration for the content of the book.
We also wish to thank Christopher J. Rogers. He checked the examples from the perspective of a beginner in the determination of the evidential value of physicochemical data. His suggestions helped to improve the quality of the practical examples contained herein.
Finally, we express our appreciation to the Institute of Forensic Research, Kraków, Poland, the Jagiellonian University, Kraków, Poland, the Escuela Politécnica Superior, Universidad Autónoma de Madrid, Spain, and the University of Edinburgh, UK, for their support of the research presented in this book.
2
Evaluation of evidence in the form of physicochemical data
2.1 Introduction
The application of numerous analytical methods to the analysis of evidence samples returns various kinds of data (Chapter 1), which should be reliable. Confirmation that the data are reliable can be obtained when the particular analytical method is validated, that is, it is confirmed by the examination and provisions of objective evidence that the particular requirements for a specific intended use are fulfilled. Parameters such as repeatability, intermediate precision, reproducibility, and accuracy should be determined during the validation process for a particular quantitative technique. Therefore, statistical quantities such as standard deviations and relative standard deviations are usually calculated, and a regression/correlation analysis as well as an analysis of variance are usually carried out during the determination of the above-mentioned parameters (Chapter 3). This means that the use of statistical tools in the physicochemical analysis of evidence should not be viewed as a passing fad, but as a contemporary necessity for the validation process of analytical methods as well as for measuring the value of evidence in the form of physicochemical data.
It should also be pointed out that in general, representatives of the administration of justice, who are not specialists in chemistry, are not interested in details such as the composition of the analysed objects, except in a situation such as the concentration of alcohol in a driver’s blood sample or the content of illegal substances in a consignment of tablets or body fluids. Therefore, results of analyses should be presented in a form that can be understood by non-specialists, but at the same time the applied method of data evaluation should express the role of a forensic expert in the administration of justice. This role is to evaluate physicochemical data (evidence, E) in the context of the prosecution proposition H1 and defence proposition H2, that is, to estimate the conditional probabilities P(E|H1) and P(E|H2) (some basic information on probability can be found in Appendix A). H1 and H2 are raised by the police, prosecutors, and the courts and they concern:
The definition of the hypotheses H1 and H2 is an important part of the process in case assessment and interpretation methodologies considering likelihood ratios (Cook et al. 1998a; Evett 2011), as it conditions the entire subsequent evidence evaluation process. In particular, propositions can be defined at different levels in a so-called hierarchy of propositions (Aitken et al. 2012; Cook et al. 1998b). The first level in the hierarchy is the source level, where the inferences of identity are made considering the possible sources of the evidence. An example of propositions at the source level for a comparison problem is as follows:
H1: the source of the glass fragments found in the jacket of the suspect is the window at the crime scene;H2: the source of the glass fragments found in the jacket of the suspect is some other window in the population of possible sources (windows).Notice that at the source level the hypotheses make no reference to whether the suspect smashed the window or not, which should be addressed at the activity level. The hypotheses considered at this level are as follows:
H1
