## The rarity of DNA profiles.(English)Zbl 1220.92044

This paper deals with a very interesting issue and questions forensic inferences methodologies in current use. Bayes’ theorem is used for analysing the so-called paternity index. The single contribution DNA profile is considered, too. A Poisson based model allows identifying a suspect. The author derives that the problem of identifying the correct person in USA is larger than 0.94 but the probability that a profile is wrongly identified is closer to one.
A similar analysis is made for genotypes using the co ancestry coefficient. Tables with the matching of two unrelated people, expectation of the number of matching pairs, and identity probabilities of common family relationships are computed. A discussion of the meaning of the results is given. The paper should encourage further studies of DNA data basis for establishing the matching probability because of the impact in forensics.

### MSC:

 92D10 Genetics and epigenetics 62P10 Applications of statistics to biology and medical sciences; meta analysis
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### References:

 [1] Anonymous (1997). DNA fingerprinting comes of age. Science 278 1407. [2] Ayres, K. L. and Overall, A. D. J. (1999). Allowing for within-subpopulation inbreeding in forensic match probabilities. Forensic Science International 103 207-216. [3] Balding, D. J. (1999). When can a DNA profile be regarded as unique? Science and Justice 39 257-260. [4] Balding, D. J. and Donnelly, P. (1995). Inference in forensic identification. J. Roy. Statist. Soc. Ser. A 158 21-53. [5] Balding, D. J. and Nichols, R. A. (1997). Significant genetic correlations among Caucasians at forensic DNA loci. Heredity 78 583-589. [6] Budowle, B. and Moretti, T. R. (1999). Genotype profiles for six population groups at the 13 CODIS short tandem repeat core loci and other PCR-based loci. Forensic Science Communications 1999 . Available at http://www.fbi.gov/hq/lab/fsc/backissu/july1999/budowle.htm. URL: [7] Diaconis, P. and Mosteller, F. (1989). Methods for studying coincidences. J. Amer. Statist. Assoc. 84 853-861. [8] Eggleston, R. (1983). Evidence , Proof and Probability , 2nd ed. Wiedenfield and Nicholson, London. [9] Fung, W. K., Carracedo, A. and Hu, Y.-Q. (2003). Testing for kinship in a subdivided population. Forensic Science International 135 105-109. [10] Galton, F. (1892). Fingerprints . MacMillan, London. [11] Kingston, C. R. (1965). Applications of probability theory in criminalistics. J. Amer. Statist. Assoc. 60 70-80. [12] Lenth, R. V. (1986). On identification by probability. J. Forensic Science Society 26 197-213. [13] Mosteller, F. (1962). Understanding the birthday problem. The Mathematics Teacher 55 322-325. [14] National Research Council (1996). The Evaluation of Forensic DNA Evidence. National Academy Press, Washington, DC. [15] Thompson, W. C. and Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials–The prosecutors fallacy and the defense attorneys fallacy. Law and Human Behavior 11 167-187. [16] Troyer, K., Gilroy, T. and Koeneman, B. (2001). A nine STR locus match between two apparent unrelated individuals using AmpFlSTR Profiler Plus$$^{\mathrm{TM}}$$ and COfiler$$^{\mathrm{TM}}$$. Proceedings of the Promega 12th International Symposium on Human Identification. [17] Weir, B. S. (1996). Genetic Data Analysis . II. Sinauer, Sunderland, MA. [18] Weir, B. S. (2004). Matching and partially-matching DNA profiles. J. Forensic Sciences 49 1009-1014. [19] Weir, B. S., Anderson, A. D. and Hepler, A. B. (2006). Genetic relatedness analysis: Modern data and new challenges. Nature Reviews Genetics 7 771-780.
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