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DNA Identification: Mixture Weight & Inference Cybergenetics © 2003-2010 Mark W Perlin, PhD, MD, PhD Cybergenetics, Pittsburgh, PA TrueAllele ® Lectures.

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Presentation on theme: "DNA Identification: Mixture Weight & Inference Cybergenetics © 2003-2010 Mark W Perlin, PhD, MD, PhD Cybergenetics, Pittsburgh, PA TrueAllele ® Lectures."— Presentation transcript:

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

2 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.

3 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 …

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

5 D16S539

6 Three Alleles Allele Quantity 500 6,

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

8 D7S820

9 Four Alleles Allele Quantity 4, ,

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

11 Overlapping Alleles

12 Template Average mean variance

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

14 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

15 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:

16 Markov Chain Monte Carlo

17 Prior Probability genotype mixture weight variance parameters DNA quantity

18 Joint Likelihood Function data pattern variation

19 Posterior Probability genotype mixture weight data variation

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

21 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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