Abstract

Is there a problem with the models used to estimate DNA match probabilities (or likelihood ratios)? For years, eminent scientists have complained that the estimates of the tiny frequencies of DNA types are unfounded. Compounding this are reports of shocking numbers of “partial matches” among samples within large DNA databases, and some scientists have complained that the infinitesimal figures used in court to estimate the probability of a random match are no better than alchemy [1]. Obviously such findings and statements damage the public perception of the credibility of DNA statistics.

Closer inspection of this problem, however, reveals that this behaviour is expected. Weir [2, 3] showed that this problem is equivalent to the classic “birthday” problem in statistics, and that the solution can be used to explain (some of) the complete matches. Weir also showed that there is additional information in the partial matches. It is possible to calculate the expected values for the partial matches as well as the complete matches, and with this information we can see how well our observations conform to this expectation.

In this talk I will discuss Weir’s solution and a proposed extension [4] which allows for the fact that any sizeable modern DNA database is likely to contain pairs of people who are full siblings (brothers), first cousins or parents/children.

References [1] David H. Kaye. Trawling DNA databases for partial matches: What is the FBI afraid of? Cornell Journal of Law and Public Policy, In Press, 2009. [2] Bruce S Weir. Matching and partially-matching DNA profiles. Journal of Forensic Sciences, 49(5):1009{1014, September 2004. PMID : 15461102. [3] Bruce S. Weir. The rarity of DNA profiles. The Annals of Applied Statistics, 1(2):358{370, 2007. [4] James M. Curran, Simon J. Walsh, and John Buckleton. Empirical testing of estimated DNA frequencies. Forensic Science International: Genetics, 1(3-4):267{272, December 2007.