The analogy between DNA kinship and DNA mixture evaluation, with applications for the interpretation of likelihood ratios produced by possibly imperfect models

A Review of Probabilistic Genotyping Systems: EuroForMix, DNAStatistX and STRmix™

“…We round out this claim by repeating Slooten's [152] statement in his Equation (5.2), which has a pedigree back to Turing (quoted in Good [153]), that the probability of obtaining an LR t from a non-donor is .…”

“…Assumption 1 fulfils Slooten's [152] requirement that "we will assume that the model … parameters are chosen independently of the hypotheses." This allows the statement that the "model cannot overstate the evidence very strongly very often for actual contributors: it cannot, averaged over all mixtures and contributors, happen with probability more than 1/t that the evidence is overstated by a factor t."…”

“…This general framework allows multiple deconvolutions, from different evidence samples that are believed to possess a common DNA donor, to be considered together in order to obtain better resolution in the genotypes of the donors to any (or multiple) of the profiles [201]. The distribution of probabilities across a number of potential genotypes (or genotype sets) can be thought of in similar ways whether considering a mixture deconvolution, or a kinship calculation [152]. Using this idea, the general framework in DBLR allows the setting-up of competing pedigrees within the evaluation [202].…”

Analysis of the Hamiltonian Monte Carlo genotyping algorithm on PROVEDIt mixtures including a novel precision benchmark

“…Probabilistic genotyping systems are required to rarely provide evidence in favour of an untrue hypothesis. Indeed, Slooten [13] noted: “To report evidence in favour of another hypothesis than the one that is actually true is not an error when the data have been correctly analysed for the relevant hypotheses, because then the data were simply misleading, but one could consider it an error, or at least very undesirable, when it is reported that there is evidence whereas there is none, due to an inadequate model having been used.”…”

“…Probabilistic genotyping systems are required to rarely provide evidence in favour of an untrue hypothesis for PoIs that are unrelated to the true contributors. Indeed, Slooten [13] noted:…”