Abstract: The Netherlands Forensic Institute has a data-base of Y-chromosome DNA profiles from a random sample of 2085 Dutch males. Within this sample, some men have the same profile as others, but most have different profiles. The sample generates the following (number theoretic) partition of the sample size: 2085 = 13 x 1 + 7 x 1+ 6 x 2 + 5 x 5 + 4 x 7 + 3 x 30 + 2 x 130 + 1 x 1650 = 13 + 7 + 6 + 6 + 5 (repeated 5 times) + .... + 2 (repeated 130 times) + 1 (repeated 1650 times).
From the body of an otherwise unidentified MH17 victim a Y-chromosome profile has been recovered. There is a missing person who we know has the same Y-chromosome profile. That profile is not present in our sample. So it is a rare profile and the match we have observed presumably constitutes pretty strong evidence that the missing person and the unidentified MH17 victim are the same. Can we quantify this?
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and for some mathematical statistical theorems
Hardy's theorem on the asymptotic number of partitions of an integer will turn out to play a crucial role in proving consistency of the "pattern maximum likelihood estimator" of the probability distribution of profiles.