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

5

Likelihood ratio models for classification problems

5.1 Introduction

In forensic cases, it is important to determine which category the object belongs to. This is a so-called classification problem, which can be solved in the context of two contrasting hypotheses: the first, H1, the proposition that the object of interest comes from category 1, while the second, H2, is the proposition that the object comes from category 2. To address this problem the likelihood ratio approach could be used in the form of in the case of discrete data, and in the case of continuous data (where P(·) stands for probability and f(·) stands for probability density function; Appendix A).

The classification problem is especially important when the objects of interest are recovered from, for example, the victim’s clothes, and there is no control sample, for example a glass fragment collected on the scene of crime. A classification of glass fragments could help investigators (policemen, prosecutors) focus their search for appropriate control materials.

It should be explained that in the forensic sphere the word classification is used to solve a problem which in statistics and chemometrics is usually referred to as discrimination. This is because discrimination in the forensic sphere is related to the problem ...