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Forensic DNA Inference ICFIS 2008 Lausanne, Switzerland Mark W Perlin, PhD, MD, PhD Joseph B Kadane, PhD Robin W Cotton, PhD Cybergenetics ©

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Likelihood Ratio quantitative rarity statistic in forensic science match likelihood ratio (MLR) posterior probability match data likelihood ratio (DLR) data data likelihood likelihood ratio ratio

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Match item questioned evidence suspect data type

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Match Probability (disjoint values) (assume types independent)

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Inner Product standard pattern comparison method widely used, powerful math properties

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Match Rarity Define the Match Likelihood Ratio (MLR) statistic

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How to compute the MLR

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MLR is a likelihood ratio Hypothesis C: suspect S contributed to evidence item Q MLR assesses match observation M under alternative contributor hypotheses C and C'

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How to report a MLR The probability of a match between evidence type Q and suspect type S is (some number) times more likely than the probability of a match between evidence type Q and a random type R.

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Type Probability likelihood function prior probability posterior probability

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Single Source DNA likelihood prior posterior

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DNA Mixture: Inclusion

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DNA Inclusion Example 21 Perpetrator [1 1], [1 2], [2 2] Suspect [2 2]

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DNA Mixture: Equality

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DNA Equality Example 21 Victim [1 1] Perpetrator [1 2], [2 2] Suspect [2 2] (obligate allele)

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Suspect S genotype probability MLR Evidence Q genotype prior probability DLR Constant Prior One Genotype DLR is a special case of MLR Mixture: Evidence Q 0/1 likelihood function

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DNA Mixture: Quantitative 1, 2 & 3 unknown low copy number damaged DNA case-to-case method validation

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DNA Kinship missing persons paternity familial search mass disaster S FM W 12

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Population Substructure Genotypes are not independent: shared ancestry Coancestry coefficient : allele IBD probability Induces a measure on joint genotypes

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Conclusions introduced MLR: "match likelihood ratio" an inner product ratio statistic agrees with "data likelihood" DNA LR extends LR to other DNA applications statistical framework for non-DNA forensics

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