4

Likelihood ratio models for comparison problems

4.1 Introduction

The comparison of physicochemical data (mostly of continuous type; Chapter 1) describing objects subjected to forensic analysis (e.g. glass fragments) is one of the most commonly encountered problems in forensic science. Data obtained from analysis of material obtained, for example, from a suspect’s clothes (the recovered sample) and from a crime scene (the control sample) may be compared. Recovered material is so called because its source is not known and it has been recovered from somewhere. Control material is so called because its source is known.

The value of evidence (E) in the form of physicochemical data can be assessed by means of the likelihood ratio (LR) approach (Section 2.2.2). This makes it possible to compare data obtained from two fragments in the context of two contrasting hypotheses. The first, termed the prosecutor’s hypothesis (H1) is the proposition that the two fragments come from the same source, while the second, termed the defence hypothesis, (H2), is the proposition that the fragments have different sources. The general LR expressions are as follows: in the case of discrete data and in the case of continuous data (where P(·) denotes probability and f(·) the probability density function; ...

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