1. DNA Identification: Quantitative Data Modeling Cybergenetics © 2003-2010 Mark W Perlin, PhD, MD, PhD Cybergenetics, Pittsburgh, PA TrueAllele ® Lectures Fall, 2010

2. Quantitative Data PCR is a linear process peak heights reflect the underlying DNA quantity use quantitative peak heights to explain the observed data

3. 1214 1314 121314 + = victim genotype second genotype? genotype pattern 12, 14 ? Genotype Model: 1 + 1 = 2 Consider all possible allele pair values by trying out each candidate

4. 1214 1314 121314 + = victim genotype second genotype? genotype pattern data 12, 14 ? Compare Model to Data

5. 1214 1314 121314 + = victim genotype second genotype? genotype pattern data Deviation Likelihood small x = 12, 14 is very likely small x large 12, 14 ?  Pr(data peak |Q=x,…) joint likelihood function Likelihood Function

6. victim genotype second genotype? genotype pattern 12, 13 ? 1314 1213 121314 = + Genotype: Alternative Value Consider a different allele pair value by trying out another candidate

7. victim genotype second genotype? genotype pattern data 12, 13 ? 1314 1213 121314 = + Compare Model to Data

8. victim genotype second genotype? genotype pattern data Deviation Likelihood small x = 12, 13 is less likely large x small 12, 13 ? 1314 1213 121314 = +  Pr(data peak |Q=x,…) joint likelihood function Likelihood Function

9. prior  likelihood  posterior All Genotype Possibilities

10. Genotype inference Pr(Q=x|data,…) posterior probability Pr(Q=x) prior probability Pr(data|Q=x,…) joint likelihood function    Try out all value possibilities; better fit's more likely it.  Pr(data locus |Q=x,…) joint likelihood function

11. Genotype probability with data uncertainty

12. Genotype alternative value

13. Bayesian probability Assess ALL genotype patterns to find the probability of each allele pair. Similarly compute the data variance. Small data variation is RESTRICTIVE: only few genotype values are possible. Large data variation is PERMISSIVE: many genotype values are possible. (more certain) (less certain)

14. Likelihood ratio match statistic reflects genotype uncertainty LR = Pr(Q=s|data) Pr(Q=s) Genotype certainty concentrates probability on just a few good bets, and focuses LR. Genotype uncertainty diffuses probability across many candidates, and reduces LR. (more info) (less info)

15. Mixture weight inference Pr(W=w|data,…) posterior probability Pr(W=w) prior probability Pr(data|W=w,…) joint likelihood function    Try out all value possibilities; better fit's more likely it.  Pr(data locus |W=w,…) joint likelihood function

16. Mixture weight probability with data uncertainty

17. Mixture weight alternative

18. Data variance inference Pr(V=v|data,…) posterior probability Pr(V=v) prior probability Pr(data|V=v,…) joint likelihood function    Try out all value possibilities; better fit's more likely it.  Pr(data peak |V=v,…) joint likelihood function

19. Data variance probability of data peak uncertainty

20. Data variance alternative

21. Quantitative data modeling genotype is main variable of interest genotype gives identification LR mixture weight is explanatory variable data variance, stochastic effects identification information preserved by quantitative modeling