title: Importance sampling allows Hdtrue tests of highly discriminating DNA profiles.
abstract: Hdtrue testing is a way of assessing the performance of a model, or DNA profile interpretation system. These tests involve simulating DNA profiles of non-donors to a DNA mixture and calculating a likelihood ratio (LR) with one proposition postulating their contribution and the alternative postulating their non-contribution. Following Turing it is possible to predict that "The average LR for the Hdtrue tests should be one"[1]. This suggests a way of validating softwares. During discussions on the ISFG software validation guidelines [2] it was argued by some that this prediction had not been sufficiently examined experimentally to serve as a criterion for validation. More recently a high profile report [3] has emphasised large scale empirical examination. A limitation with Hdtrue tests, when non-donor profiles are generated at random (or in accordance with expectation from allele frequencies), is that the number of tests required depends on the discrimination power of the evidence profile. If the Hdtrue tests are to fully explore the genotype space that yields non-zero LRs then the number of simulations required could be in the 10s of orders of magnitude (well outside practical computing limits). We describe here the use of importance sampling, which allows the simulation of rare events to occur more commonly than they would at random, and then adjusting for this bias at the end of the simulation in order to recover all diagnostic values of interest. Importance sampling, whilst having been employed by others for Hdtrue tests, is largely unknown in forensic genetics. We take time in this paper to explain how importance sampling works, the advantages of using it and its application to Hdtrue tests. We conclude by showing that employing an importance sampling scheme brings Hdtrue testing ability to all profiles, regardless of discrimination power.
authors.affiliation: Forensic Science South Australia, 21 Divett Place, Adelaide, SA 5000, Australia; School of Biological Sciences, Flinders University, GPO Box 2100 Adelaide SA, Australia 5001 ESR, Private Bag 92021, Auckland 1142, New Zealand. Electronic address: Duncan.Taylor@sa.gov.au.
authors.forename: Duncan
authors.initials: D
authors.lastname: Taylor
authors.affiliation: Department of Statistics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand.
authors.forename: James M
authors.initials: JM
authors.lastname: Curran
authors.affiliation: National Institute of Standards and Technology, 100 Bureau Drive, MS 8980 and 8314, Gaithersburg, MD 20899, United States; ESR, Private Bag 92021, Auckland 1142, New Zealand.
authors.forename: John
authors.initials: J
authors.lastname: Buckleton
mesh_terms: D016172:DNA Fingerprinting; D005838:Genotype; D006801:Humans; D016013:Likelihood Functions; D008957:Models, Genetic
keywords: DNA profile; H(d) true; Importance sampling; Likelihood ratios; Performance tests