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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!