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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) P E Hp L P E Hd 1 L P CprofileA SprofileA • 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: 2 Theta P aa aa 1 Theta Pa 3 Theta 1 Theta 1 1 Theta Pa 2 Theta – 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) = 0.0338462 – The new Pa = Sqrt[P(aa)] = 0.18397 – L2 = (L1) (5.582886 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. Pa 1 Pa Panew Pa Zc N – 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 = 10000 • Zc = 3 (99.73% - Really greater, approx 99.86%) • New Pa = 0.103 • L3 = (L1)(0.5874) Effects of human error: Example: N = 10000 (number of cases) PoliceError = 0.02 LabError = 0.001 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!