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Improving Forensic Identification in Bayesian Networks : Accounting for Population SubstructurePowerPoint Presentation

Improving Forensic Identification in Bayesian Networks : Accounting for Population Substructure

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Improving Forensic Identification in Bayesian Networks : Accounting for Population Substructure

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Improving Forensic Identification in Bayesian Networks : Accounting for Population Substructure

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Improving Forensic Identification in Bayesian Networks :Accounting for Population Substructure

Amanda B. Hepler

- Population Substructure (PS)
- Bayesian Networks
- Introduction
- Incorporating PS into Paternity Networks
- Example

- Any deviation from random mating
- Commonly due to geographical subdivision
- Mating pairs often have remote relatives in common
- Inbreeding coefficient ():
- measures the extent of common ancestry

- Ignoring PS “would unfairly overstate the strength of the evidence against the defendant.” (Balding & Nichols, 1995)
- “If the allele frequencies for the subgroup are not available…[forensic] calculations should use the population-structure equations.” (1996 NRC Report)

- Population allele frequencies are known
- Inbreeding coefficient is known
- Loci are independent
- Within a subpopulation:
- Mating is random
- Migration and mutation events independent and constant

Graphical Portion

Hair Color

Eye Color

Red

0.5

Hair Color:

Red

Brown

Numerical Portion

Brown

0.5

Blue

0.2

0.9

Green

0.8

0.1

- A graphical model that expresses probabilistic relationships among variables or events1

- HUGIN used to create BNs, free version available at http://www.hugin.dk

BNs provide:

- Simple representations of complex problems
- Automation of complex algebraic manipulations
- Communication aide

- M = mother, C = child, PF = putative father
- Hp: PF is the father of CHd: Some other man is the father of C
- Likelihood ratio, or paternity index (PI):
- Interpretation: “The evidence is PI times more probable if PF is the father of C than if some other man is the father.”

Genotype Nodes(A1A1, A1A2, A2A2)

Mother

Putative Father

Allele/Gene Nodes(A1, A2)

Child

- One locus, two alleles: A1and A2
- Observe genotypes of M, C, and PF

PF’s Maternal Gene

PF’s Paternal Gene

PF’s Genotype

Hypothesis Node (Yes, No)

- A.P. Dawid, J. Mortera, V.L. Pascali, and D. Van Boxel. Probabilistic expert systems for forensic inference from genetic markers. Scandinavian Journal of Statistics, 29:577-595. 2002.

- Probability of allele Aidepends on how many Aialready observed
- Modified allele frequencies3:

- pi = frequency of the ith allele in the pop’n
- ni = number of observed alleles of type Ai
- n = total number of alleles observed

- D.J. Balding and R.A. Nichols. DNA profile match probability calculation. Forensic Science International, 64(2-3):125-140, 1994.

- :p1:
- Keep track of founder genes:
- Counting nodes:
is the value of n1 after founder 2

is the value of n1 after founder 3, etc.

now depends on

- θ = 0.03, p1 = 0.10
- M = A1A1, C = A1A1, PF = A1A2
- PIfor this case4:

- I.W. Evett and B.S. Weir. Interpreting DNA Evidence. Sinauer, Sunderland,MA., 1998.

This same result can be obtained using HUGIN:

- Assume no population substructure (θ = 0):

- 2.91 more “conservative” than 5.00

- Multiple loci case:
- Assume loci independent
- Multiply PI

- Multiple Allele Case:
- M and PF have at most four distinct alleles

- Missing Father Case:
- Brother’s genotype available

- Apply same methodology to other BNs:
- Mutation
- Cross-Transfer Evidence
- Mixtures
- Remains Identification

- Software improvements
- Need software for the forensic scientist
- Improvements needed for run time