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DNA Identification: Mixture Weight & Inference Cybergenetics © Mark W Perlin, PhD, MD, PhD Cybergenetics, Pittsburgh, PA TrueAllele ® Lectures Fall, 2010

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Mixture Weight: Uncertain Quantity Infer mixture weight from STR experiments: quantitative peak data contributor genotypes Pr(W=w | data, G 1 =g 1, G 2 =g 2, …) hierarchical Bayesian model Perlin MW, Legler MM, Spencer CE, Smith JL, Allan WP, Belrose JL, Duceman BW. Validating TrueAllele ® DNA mixture interpretation. Journal of Forensic Sciences. 2011;56(November):in press.

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Mixture Weight Model template weight locus weights WkWk W k,1 W k,2 W k,N … k th contributor W0W0 prior probability experiment data d k,1 d k,2 d k,N …

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Experiment Estimate wkwk sum of peak heights from k th contributor sum of peak heights from all contributors =

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D16S539

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Three Alleles Allele Quantity 500 6,

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Experiment Estimate Allele Quantity 500 6, , ,500 = 10%=

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D7S820

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Four Alleles Allele Quantity 4, ,

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Experiment Estimate , , ,500 = 6.7%= Allele Quantity 4, ,

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Overlapping Alleles

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Template Average mean variance

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Template Mixture Weight Probability Distribution mean = 6.7% standard deviation = 0.9%

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Central Limit Theorem more data experiments for a template provide greater mixture weight precision double the precision by doing four times the number of experiments combine evidence from multiple experiments to obtain a more informative result

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Probability Solution w | d, g 1, g 2, … g 1 | d, g 2, w, … g 2 | d, g 1, w, … interacting random variables find probability distributions by iterative sampling z i | d, g 1, g 2, w, … Gelfand, A. and Smith, A. (1990). Sampling based approaches to calculating marginal densities. J. American Statist. Assoc., 85:

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Markov Chain Monte Carlo

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Prior Probability genotype mixture weight variance parameters DNA quantity

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Joint Likelihood Function data pattern variation

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Posterior Probability genotype mixture weight data variation

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Generally Accepted Method genotype mixture weight data variation James Curran. A MCMC method for resolving two person mixtures. Science & Justice. 2008;48(4):

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Hierarchical Bayesian Model with MCMC Solution standard approach in modern science describes uncertainty using probability the "new calculus" replaces hard calculus with easy computing can solve virtually any problem well-suited to interpreting DNA evidence

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