Dimensionality reduction of multielement glass evidence to calculate likelihood ratios

Abstract

AbstractDimensionality reduction of multivariate elemental concentrations of glass is reported for computing likelihood ratios (LRs). The LRs calculated using principal component analysis (PCA) and a post hoc calibration steps result in very low (<1%) false inclusions when comparing glass samples known to originate from different sources and very low (<1%) false exclusions when comparing glass samples known to originate from the same source. The LRs calculated using the novel PCA approach are compared with previously reported LRs calculated using a more computationally intensive Multivariate Kernel (MVK) model followed by a calibration step using a Pool Adjacent Violators (PAV) algorithm. In both cases, the calibrated LRs limited the magnitude of the misleading evidence, providing only weak to moderate support for the incorrect hypotheses. Most of the different pairs that were found to be falsely included were explained by chemical relatedness (same manufacturer of the glass sources in very close time interval between manufacture). The computation of LRs using dimensionality reduction of elemental concentrations using PCA may transfer to other multivariate data‐generating evidence types.