Statistical Analysis in Forensic Science Evidential Value of Multivariate Physicochemical Data

by Zadora, Grzegorz; Martyna, Agnieszka; Ramos, Daniel; Aitken, Colin

• ISBN13: 9780470972106
• ISBN10: 0470972106
• Edition: 1st
• Format: Hardcover
• Copyright: 2014-02-03
• Publisher: Wiley

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. 

Author Biography

Grzegorz Zadora, Institute of Forensic Research, Krakow, Poland.

Daniel Ramos, Telecommunication Engineering, Universidad Autonoma de Madrid, Spain.

Table of Contents

Preface xiii

1 Physicochemical data obtained in forensic science laboratories 1

1.1 Introduction 1

1.2 Glass 2

1.2.1 SEM-EDX technique 4

1.2.2 GRIM technique 5

1.3 Flammable liquids: ATD-GC/MS technique 8

1.4 Car paints: Py-GC/MS technique 10

1.5 Fibres and inks: MSP-DAD technique 13

References 15

2 Evaluation of evidence in the form of physicochemical data 19

2.1 Introduction 19

2.2 Comparison problem 21

2.2.1 Two-stage approach 21

2.2.2 Likelihood ratio approach 23

2.2.3 Difference between an application of two-stage approach and likelihood ratio approach 26

2.3 Classification problem 27

2.3.1 Chemometric approach 27

2.3.2 Likelihood ratio approach 31

2.4 Likelihood ratio and Bayes’ theorem 31

References 32

3 Continuous data 35

3.1 Introduction 35

3.2 Data transformations 37

3.3 Descriptive statistics 39

3.3.1 Measures of location 39

3.3.2 Dispersion: Variance estimation 42

3.3.3 Data distribution 44

3.3.4 Correlation 45

3.3.5 Continuous probability distributions 49

3.4 Hypothesis testing 59

3.4.1 Introduction 59

3.4.2 Hypothesis test for a population mean for samples with known variance σ2 from a normal distribution 60

3.4.3 Hypothesis test for a population mean for small samples with unknown variance σ2 from a normal distribution 63

3.4.4 Relation between tests and confidence intervals 67

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 68

3.4.6 Paired comparisons 72

3.4.7 Hotelling’s T 2 test 75

3.4.8 Significance test for correlation coefficient 77

3.5 Analysis of variance 78

3.5.1 Principles of ANOVA 78

3.5.2 Feature selection with application of ANOVA 82

3.5.3 Testing of the equality of variances 85

3.6 Cluster analysis 85

3.6.1 Similarity measurements 86

3.6.2 Hierarchical cluster analysis 89

3.7 Dimensionality reduction 92

3.7.1 Principal component analysis 93

3.7.2 Graphical models 99

References 105

4 Likelihood ratio models for comparison problems 107

4.1 Introduction 107

4.2 Normal between-object distribution 108

4.2.1 Multivariate data 109

4.2.2 Univariate data 110

4.3 Between-object distribution modelled by kernel density estimation 110

4.3.1 Multivariate data 111

4.3.2 Univariate data 111

4.4 Examples 112

4.4.1 Univariate research data – normal between-object distribution – R software 112

4.4.2 Univariate casework data – normal between-object distribution – Bayesian network 116

4.4.3 Univariate research data – kernel density estimation – R software 119

4.4.4 Univariate casework data – kernel density estimation – calcuLatoR software 125

4.4.5 Multivariate research data – normal between-object distribution – R software 127

4.4.6 Multivariate research data – kernel density estimation procedure – R software 129

4.4.7 Multivariate casework data – kernel density estimation – R software 137

4.5 R Software 140

4.5.1 Routines for casework applications 140

4.5.2 Routines for research applications 144

References 149

5 Likelihood ratio models for classification problems 151

5.1 Introduction 151

5.2 Normal between-object distribution 152

5.2.1 Multivariate data 153

5.2.2 Univariate data 153

5.2.3 One-level models 154

5.3 Between-object distribution modelled by kernel density estimation 155

5.3.1 Multivariate data 155

5.3.2 Univariate data 156

5.3.3 One-level models 156

5.4 Examples 157

5.4.1 Univariate casework data – normal between-object distribution – Bayesian network 158

5.4.2 Univariate research data – kernel density estimation procedure – R software 161

5.4.3 Multivariate research data – kernel density estimation – R software 164

5.4.4 Multivariate casework data – kernel density estimation – R software 169

5.5 R software 172

5.5.1 Routines for casework applications 172

5.5.2 Routines for research applications 175

References 179

6 Performance of likelihood ratio methods 181

6.1 Introduction 181

6.2 Empirical measurement of the performance of likelihood ratios 182

6.3 Histograms and Tippett plots 183

6.4 Measuring discriminating power 186

6.4.1 False positive and false negative rates 187

6.4.2 Discriminating power: A definition 188

6.4.3 Measuring discriminating power with DET curves 190

6.4.4 Is discriminating power enough? 192

6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots 192

6.5.1 Accuracy in a classical example: Weather forecasting 193

6.5.2 Calibration 195

6.5.3 Adaptation to forensic inference using likelihood ratios 196

6.6 Comparison of the performance of different methods for LR computation 200

6.6.1 MSP-DAD data from comparison of inks 200

6.6.2 Py-GC/MS data from comparison of car paints 205

6.6.3 SEM-EDX data for classification of glass objects 209

6.7 Conclusions: What to measure, and how 214

6.8 Software 215

References 216

Appendix A Probability 218

A.1 Laws of probability 218

A.2 Bayes’ theorem and the likelihood ratio 222

A.3 Probability distributions for discrete data 225

A.4 Probability distributions for continuous data 227

References 227

Appendix B Matrices: An introduction to matrix algebra 228

B.1 Multiplication by a constant 228

B.2 Adding matrices 229

B.3 Multiplying matrices 230

B.4 Matrix transposition 232

B.5 Determinant of a matrix 232

B.6 Matrix inversion 233

B.7 Matrix equations 235

B.8 Eigenvectors and eigenvalues 237

Reference 239

Appendix C Pool adjacent violators algorithm 240

References 243

Appendix D Introduction to R software 244

D.1 Becoming familiar with R 244

D.2 Basic mathematical operations in R 246

D.2.1 Vector algebra 248

D.2.2 Matrix algebra 250

D.3 Data input 252

D.4 Functions in R 254

D.5 Dereferencing 255

D.6 Basic statistical functions 257

D.7 Graphics with R 258

D.7.1 Box-plots 258

D.7.2 Q-Q plots 259

D.7.3 Normal distribution 260

D.7.4 Histograms 262

D.7.5 Kernel density estimation 263

D.7.6 Correlation between variables 263

D.8 Saving data 266

D.9 R codes used in Chapters 4 and 5 266

D.9.1 Comparison problems in casework studies 266

D.9.2 Comparison problems in research studies 273

D.9.3 Classification problems in casework studies 278

D.9.4 Classification problems in research studies 285

D.10 Evaluating the performance of LR models 289

D.10.1 Histograms 289

D.10.2 Tippett plots 290

D.10.3 DET plots 291

D.10.4 ECE plots 292

Reference 293

Appendix E Bayesian network models 294

E.1 Introduction to Bayesian networks 294

E.2 Introduction to Hugin ResearcherTM software 296

E.2.1 Basic functions 297

E.2.2 Creating a new Bayesian network 298

E.2.3 Calculations 302

References 308

Appendix F Introduction to calcuLatoR software 309

F.1 Introduction 309

F.2 Manual 309

Reference 314

Index 315