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Score-based Likelihood Ratio Properties for the Specific-Source Identification Problem

NCJ Number
Date Published
July 2023
13 pages

This paper discusses the use of a core-based likelihood ratio (SLR) to address the specific-source identification problem.


In the identification of source problem, a likelihood ratio (LR) is used to quantify the value of evidence under two competing models for how the evidence has arisen. When the feature space of this evidence is very complex, a score-based likelihood ratio (SLR) can be used as a surrogate for the value of evidence. Utilizing a SLR results in the use of simpler underlying densities due to the score function mapping the complex evidence to a univariate score; however, it is expected that some information is lost when using a score. Hence, the SLR can perform slightly differently than the LR. The authors discuss four reasonable properties that should be expected of a SLR when used for the specific source identification problem: first, that the SLR can be constructed when the background population consists of one alternative source; second, when the background population consists of a single alternative source, and the researchers invert the role of the specific source and the alternative source, the full SLR is also inverted; third, when the alternative source population is composed of multiple sources, the inverse of the omnibus SLR can be written in terms of the average of the inverse of the simple SLR, where the simple SLR is the SLR of the specific source vs one alternative source; and finally, that the SLR does not provide stronger support for either model than a LR. These properties will be formally written and demonstrated on trace element concentrations in aluminum foil sources. 

Date Published: July 1, 2023