Evaluation of Trace Evidence in the Form of Multivariate Data

Abstract

The evaluation of measurements on characteristics of trace evidence found at a crime scene and on a suspect is an important part of forensic science. Five methods of assessment for the value of the evidence for multivariate data are described. Two are based on significance tests and three on the evaluation of likelihood ratios. The likelihood ratio which compares the probability of the measurements on the evidence assuming a common source for the crime scene and suspect evidence with the probability of the measurements on the evidence assuming different sources for the crime scene and suspect evidence is a well-documented measure of the value of the evidence. One of the likelihood ratio approaches transforms the data to a univariate projection based on the first principal component. The other two versions of the likelihood ratio for multivariate data account for correlation among the variables and for two levels of variation: that between sources and that within sources. One version assumes that between-source variability is modelled by a multivariate normal distribution; the other version models the variability with a multivariate kernel density estimate. Results are compared from the analysis of measurements on the elemental composition of glass. Copyright 2004 Royal Statistical Society.

Transformations for compositional data with zeros with an application to forensic evidence evaluation

“…Under Model 2, which utilises kernel density estimation for the betweenobject distribution, the numerator (5) and the denominator (7) of the likelihood ratio are estimated using multivariate Gaussian kernels with bandwidth matrix H. This matrix was estimated in two different ways: KDE1 -Following [4], assume that H is of the form h 2 C and use a rule-of-thumb formula based on [20] for estimating h:…”

“…Note that expression (5) is a simplified version of the corresponding equation in [4], which uses a bandwidth matrix of the form H = h 2 C. Similarly, under Model 2 the denominator of the likelihood ratio, for which H d is assumed true, can be shown to be given by:…”

Hybrid approach combining chemometrics and likelihood ratio framework for reporting the evidential value of spectra

“…When KDE is applied for modelling the between-object distribution, it takes the form 440 [4,2,36]: The diagonals of the matrices archive the true H 1 LR values (expected to be greater than 1) for comparing the objects sharing the same origins (estimation of false negative answers), whereas gray areas below or above the diagonals store the true H 2 LR values (expected to be lower than 1) for comparing the objects with different origins (estimation of false positive answers).…”

“…Therefore, when kernel density estimation is applied for modelling the betweenobject distribution, the numerator could be expressed by [4,2,36]:…”

Exact solutions to Bayesian and maximum likelihood problems in facial identification when population and error distributions are known

“…A novel and complex score-normalization technique, KL-Tnorm, was developed as an aid to automatic speaker recognition [6]. In addition, a group at the University of Edinburgh led by Professor Colin Aitken has carried out important and pioneering work in the application of multivariate analysis to the development of significance tests and likelihood ratios (LRs) for the assessment of trace evidence, such as glass fragments found at a crime scene and on a suspect [7]. This paper addresses one of this group of problems, namely that of identifying faces from photographs, such as stills taken from CCTV video footage.…”