Probability and Statistics of DNA Fingerprinting

(posterior odds) = (likelihood ratio) (prior odds) The “strength” of a piece of evidence includes: –Its accuracy. –Its meaning. DNA evidence merely tries to connect or disconnect a piece of evidence to a suspect. It makes NO assertions of guilt or innocence!!!

(Weir, slide 26) Key questions: –The “event” is that a piece of DNA evidence matches the DNA of the suspect: How likely is this evidence to have that type, if it comes from the suspect? (prosecution) How likely is this evidence to have that type, if it comes from someone else? (defense)

(Weir, slide 27)

Assuming independence in the allele frequencies: –Example: 18 alleles, each with a frequency of Pa = 0.1. –L1 = 1 / (Pa ^ 18) –L1 = 10^18

(Weir, slide 35) Allele frequency dependence due to evolution: –Dealing with pairs of alleles. –Theta is the probability that two alleles, each from a different randomly selected person, are identical due to evolutionary means.

Assuming dependence in the allele frequencies due to evolution: –Example: 18 alleles Pa = 0.1 Theta = 0.04 –P(aa) = –The new Pa = Sqrt[P(aa)] = –L2 = (L1) ( x 10^-4)

Adjustments of allele frequencies due to sampling effects: –Can’t make a DNA profile of everyone! –Must estimate how inaccurate your DNA database might be. –Zc is in terms of standard deviations –N is the number of alleles at the specific locus in the database (confidence interval for proportions for an infinite binomial population)

Adjustments in allele frequencies due to sampling limitations: –Example: Pa = 0.1 N = Zc = 3 (99.73% - Really greater, approx 99.86%) New Pa = L3 = (L1)(0.5874)

Effects of human error: Example: N = (number of cases) PoliceError = 0.02 LabError = DNATestError = 1/(some L) = 1/(50 x 10^6) (1-PoliceError)(1-LabError)(1-DNATestError) = (1-PoliceError)(1-LabError) approx. Human Error is overwhelming the deciding factor with the accuracy of DNA fingerprinting!

Conclusions –Human error is the overwhelming factor in the accuracy of DNA fingerprinting. (However, its involved in all forms of evidence.) –Allele frequencies are NOT independent of each other. However when evolutionary considerations and sampling considerations are taken into account, the accuracy of DNA fingerprinting is still “beyond human experience”. –A statement of the accuracy of some piece of DNA evidence, by itself, is NOT a statement of guilt of innocence!