Likelihood ratio estimation of partial Y-STR profile matches using discrete Laplace models and marginalisation

The discrete Laplace model can be used to estimate the evidential weight of a match between the Y-chromosome short tandem repeat (Y-STR) DNA profiles of the evidence material and a suspect. When the weight of evidence of a match between partial Y-STR profiles is assessed, a discrete Laplace model, restricted to the observed loci in the partial evidence profile, is constructed. However, fitting such a discrete Laplace model is time-consuming since it requires estimating the parameters of the discrete Laplace model and validating the model. We implemented the marginalisation method for discrete Laplace models to estimate the evidential weight of a match between a partial Y-STR evidence profile and a Y-STR reference profile. Since the marginalisation method is based on discrete Laplace models for complete Y-STR profiles, no additional models need to be constructed. We compared the likelihood ratios (LRs) obtained with (1) the marginalisation method and (2) by fitting new discrete Laplace models restricted to the observed loci in the partial evidence profile. In most cases, the two methods yielded similar LRs, differing by a factor less than 10. Although rare, large differences in the LRs obtained from the two methods were also observed. If all LRs were restricted to at most 1,000,000, then ca. 1.8%, 0.16%, and 0.007% of the cases resulted in differences in LRs between the two methods that were larger than factors of 10,100, and 1,000, respectively. Given the similar performance of the two methods, the reduced computational cost of the marginalisation method makes it a more practical and time-efficient choice for forensic applications.