Statistical Analysis in Forensic Science

Preface xiii 1 Physicochemical data obtained in forensic science laboratories 1 1.1 Introduction 1 1.2 Glass 2 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 2.3 Classification problem 27 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 3.4 Hypothesis testing 59 3.5 Analysis of variance 78 3.6 Cluster analysis 85 3.7 Dimensionality reduction 92 References 105 4 Likelihood ratio models for comparison problems 107 4.1 Introduction 107 4.2 Normal between-object distribution 108 4.3 Between-object distribution modelled by kernel density estimation 110 4.4 Examples 112 4.5 R Software 140 References 149 5 Likelihood ratio models for classification problems 151 5.1 Introduction 151 5.2 Normal between-object distribution 152 5.3 Between-object distribution modelled by kernel density estimation 155 5.4 Examples 157 5.5 R software 172 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 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots 192 6.6 Comparison of the performance of different methods for LR computation 200 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.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.8 Saving data 266 D.9 R codes used in Chapters 4 and 5 266 D.10 Evaluating the performance of LR models 289 Reference 293 Appendix E Bayesian network models 294 E.1 Introduction to Bayesian networks 294 E.2 Introduction to Hugin ResearcherTM software 296 References 308 Appendix F Introduction to calcuLatoR software 309 F.1 Introduction 309 F.2 Manual 309 Reference 314 Index 315