Probability and Statistics of DNA Fingerprinting

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Probability and Statistics of DNA Fingerprinting
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• (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!!!

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• (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)

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• (Weir, slide 27)

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• Assuming independence in the allele frequencies
• Example
• 18 alleles, each with a frequency of Pa 0.1.
• L1 1 / (Pa 18)
• L1 1018

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• (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.

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• 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 SqrtP(aa) 0.18397
• L2 (L1) (5.582886 x 10-4)

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• Adjustments of allele frequencies due to sampling
  effects
• Cant 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)

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• 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)

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• Effects of human error
• Example
• N 10000 (number of cases)
• PoliceError 0.02
• LabError 0.001
• DNATestError 1/(some L) 1/(50 x 106)
• (1-PoliceError)(1-LabError)(1-DNATestError)
• (1-PoliceError)(1-LabError) approx.
• Human Error is overwhelming the deciding factor
  with the accuracy of DNA fingerprinting!

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• 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!