Efficient construction of match strength distributions for uncertain multi-locus genotypes

Abstract

Natural variation in biological evidence leads to uncertain genotypes. Forensic comparison of a probabilistic genotype with a person's reference gives a numerical strength of DNA association. The distribution of match strength for all possible references usefully represents a genotype's potential information. But testing more genetic loci exponentially increases the number of multi-locus possibilities, making direct computation infeasible.At each locus, Bayesian probability can quickly assemble a match strength random variable. Multi-locus match strength is the sum of these independent variables. A multi-locus genotype's match strength distribution is efficiently constructed by convolving together the separate locus distributions. This convolution construction can accurately collate all trillion trillion reference outcomes in a fraction of a second.This paper shows how to rapidly construct multi-locus match strength distributions by convolution. Function convergence demonstrates that distribution accuracy increases with numerical resolution. Convolution construction has quadratic computational complexity, relative to the exponential number of reference genotypes. A suitably defined random variable reduces high-dimensional computational cost to fast real-line arithmetic.Match strength distributions are used in forensic validation studies. They provide error rates for match results. The convolution construction applies to discrete or continuous variables in the forensic, natural and social sciences. Computer-derived match strength distributions elicit the information inherent in DNA evidence, often overlooked by human analysis.

Validating TrueAllele® Interpretation of DNA Mixtures Containing up to Ten Unknown Contributors

“…Conditioned on a match statistic, the probability of misleading evidence (PME) for uncertain genotypes gave the chance that a noncontributor had a match statistic at least as large as the one observed . While the chance of a positive noncontributor log(LR) was 1% for five or six contributors, the PME dropped to 0.05% with log(LR) over 2 ban (Table S2b).…”

“…These observations are consistent with the linear relationship between log(LR) match information and DNA quantity. A validation specificity distribution is the average of its component probabilistic genotype specificity distributions . Therefore, DNA amount determines the log(LR) distribution’s center, while genotype uncertainty sets the distribution’s spread.…”

Commentary on: Thompson WC. Uncertainty in probabilistic genotyping of low template DNA: A case study comparing STRmix™ and TrueAllele®. J Forensic Sci. 2023;68(3):1049–63

“…TrueAllele constructs high-resolution LR distributions [9] for calculating LR error rates. This comprehensive method supports both false-positive rates for inclusionary match statistics, and falsenegative rates for exclusionary results [10,11].…”