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Probability and Statistics of DNA Fingerprinting

Probability and Statistics of DNA Fingerprinting. (posterior odds) = (likelihood ratio) (prior odds) The “strength” of a piece of evidence includes: Its accuracy. Its meaning.

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Probability and Statistics of DNA Fingerprinting

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  1. Probability and Statistics of DNA Fingerprinting

  2. (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!!!

  3. (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)

  4. (Weir, slide 27)

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

  6. (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.

  7. 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)

  8. 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)

  9. 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)

  10. 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!

  11. 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!

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