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Multi-Element Comparisons of Tapes Evidence Using Dimensionality Reduction for Calculating Likelihood Ratios

NCJ Number
Anjali Gupta; Claudia Martinez-Lopez; James M. Curran; Jose R. Almirall
Date Published
August 2019
9 pages
Since computing the likelihood ratio (LR) as a measure of weight of evidence has traditionally been difficult for multi-element evidence, the current study sought to reduce the dimensionality of the problem by using principal component analysis (PCA) and a post-hoc calibration step suggested by van Es et al., and evaluated the performance of this method by using multi-element data collected from electrical tapes with up to 18 elements measured.
A set of 90 tapes known to originate from different sources were analyzed by LA-ICP-MS. Additive log-ratio transformation was used with respect to the signal of 208Pb to transform the 18-dimensional data. This transformation altered the scale of the signals; and more importantly, the transformed signals exhibited characteristics similar to a normal distribution. Scores of the first five principal components (PCs) were used as input to the LR formula given by Aitken and Lucy where it was assumed multivariate normal between-sources distribution (LR MVN) to compare the tapes. The study found that the calculated LRs were extremely positive and negative and did not conform with the definition of well-calibrated LRs. Thus, the researchers used the post-hoc calibration method given by van Es et al. to calibrate the likelihood ratios. The calibrated LRs were obtained within an appropriate range. Five scenarios, each related to the number of principal components used to compare the samples, formed part of this study. The first scenario made the comparisons using only the first PC; the second scenario used the first two PCs together and so on. The last scenario, LR5, used five PCs for the comparisons. Comparing the results of these five scenarios provided an understanding around sensitivity of the method based on the percentage of information used for the comparisons. The lowest false exclusion (Type I) and false inclusion (Type II) error rates were obtained for LR5 scenario in comparison to all the other scenarios. False inclusion and false exclusion error rates of 3.7 percent and 2.2 percent were reported by using only 5 out of 17 PCs. False exclusion error rates of 2.2 percent indicated that only two same-source comparisons had LR < 1. The proposed method overcomes the problem of using highly-dimensional data for the comparisons, while using a high percentage of information present in the original data. (publisher abstract modified)

Date Published: August 1, 2019