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

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Presentation transcript:

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

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

= victim genotype second genotype? genotype pattern 12, 14 ? Genotype Model: = 2 Consider all possible allele pair values by trying out each candidate

= victim genotype second genotype? genotype pattern data 12, 14 ? Compare Model to Data

= 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

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

victim genotype second genotype? genotype pattern data 12, 13 ? = + Compare Model to Data

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

prior  likelihood  posterior All Genotype Possibilities

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

Genotype probability with data uncertainty

Genotype alternative value

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)

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)

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

Mixture weight probability with data uncertainty

Mixture weight alternative

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

Data variance probability of data peak uncertainty

Data variance alternative

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