1. DNA Identification: Mixture Weight & Inference
Mark W Perlin, PhD, MD, PhD
Cybergenetics, Pittsburgh, PA
TrueAllele® Lectures
Fall, 2010
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2. Mixture Weight: Uncertain Quantity
Infer mixture weight from
STR experiments:
• quantitative peak data
• contributor genotypes
Pr(W=w | data, G1=g1, G2=g2, …)
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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3. Mixture Weight Model kth contributor experiment data dk,1 dk,2 … dk,N
locus weights
Wk,1
Wk,2 …
Wk,N
template weight Wk
prior probability W0
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4. Experiment Estimate sum of peak heights from kth contributor wk =
from all contributors
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5. D16S539
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6. Three Alleles Allele 11 12 13 Quantity 500 6,750 250 11 12 13
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7. Experiment Estimate Allele 11 12 13 Quantity 500 6,750 250 500 + 250,
750 11 12 13 =
= 10%
7,500
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8. D7S820
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9. Four Alleles Allele 8 10 12 13 Quantity 4,000 250 3,000 8 10 12 13
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10. Experiment Estimate Allele 8 10 12 13 Quantity 4,000 250 3,000
4, , 8 10 12 13
500 =
= 6.7%
7,500
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11. Overlapping Alleles
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12. Template Average
mean
variance
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13. Template Mixture Weight Probability Distribution
mean = 6.7%
standard
deviation
= 0.9%
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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
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15. Probability Solution interacting random variables w | d, g1, g2, …
g1 | d, g2, w, …
g2 | d, g1, w, …
zi | d, g1, g2, w, …
find probability distributions by iterative sampling
Gelfand, A. and Smith, A. (1990). Sampling based approaches to calculating marginal densities. J. American Statist. Assoc., 85:
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16. Markov Chain Monte Carlo

17. Prior Probability genotype mixture weight DNA quantity variance
parameters

18. Joint Likelihood Function
data
pattern
variation

19. Posterior Probability
genotype
mixture weight
data variation

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

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