Hot Off the Presses: Beyond Uniqueness

The Birthday Problem, a classic puzzler of probability theory, has a counter-intuitive answer. Statisticians on the National Academy of Sciences' Committee on Forensic DNA Evidence: An Update, used the problem to distinguish two arguments that might support the conclusion that DNA types are unique in a population. Years later, law and business school professor Jay Koehler used the same problem to show how difficult it is to demonstrate total uniqueness -- and what other kind is there? -- of toolmarks on the basis of the collective experience of toolmark examiners. A report of a NIST (National Institute of Standards and Technology) expert working group on latent fingerprint analysis also invoked the problem to explain why even a tiny random match probability does not establish that fingerprint images are discernibly unique. Nevertheless the Birthday Problem cannot refute a claim that examiners making source attributions from almost unique features will almost never be wrong. (Of course, this observation does not mean that a claim of almost no errors in case work would be true.)

The relationship between a small number of duplicates and individualization in the sense of source attribution was the subject of a paper presented at the Eighth International Conference on Forensic Statistics in 2011. An updated version of the paper appeared this month as Beyond Uniqueness: The Birthday Paradox, Source Attribution, and Individualization in Forensic Science Testimony, Law, Probability and Risk, Vol. 12, March 2013, pp. 3-11. Regrettably, the publisher, Oxford University Press, forbids authors from posting the final versions of articles in the journal, but an earlier draft is available on SSRN.

Abstract: For many decades, forensic science identification experts have insisted that they can ‘individualize’ traces such as fingerprints and toolmarks to the one and only one object that produced them. They have relied on a theory of global uniqueness of patterns as the basis for such individualization. Although forensic practitioners and theorists are moving toward a more probabilistic understanding of pattern matching, textbooks and reference works continue to assert that uniqueness justifies individualization and that experience demonstrates discernible uniqueness. One response to the last claim applies a famous problem in probability theory — the Birthday Problem — to the forensic realm to show that even an extensive record of uniqueness does little to prove that all such patterns are unique. This essay describes the probabilistic reasoning and its limits. It argues that the logic of the Birthday Paradox does indeed undercut the theory of global, general uniqueness, but that the reasoning is logically compatible with opinion testimony that a specific object is nearly certain to be the source of a pattern or trace. It also notes some alternatives to categorical claims of individualization, whether those claims are based on the theory of global, general uniqueness or instead on some less sweeping and more defensible theory.