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Elicitation of Priors in Bayesian
Modeling of Forensic DNA Evidence
William C. Thompson
University of California, Irvine
When should forensic
scientists consider priors?
• Never?
– Invades province of trier-of-fact
• When a prior is needed to estimate LR
– “Subsidiary prior”
– Issues: Whose prior? Based on what? Elicited how?
• When modeling whole cases
– For benefit of court (e.g., Alkemada)
– To explore properties of evidence (e.g., novelty effect)
• To apply a categorical reporting threshold???
The Murderer’s Cap
• Clerk of convenience store
is shot and killed by man
wearing a white cap
• Killer flees, leaving white
“Clemson Tiger” cap at
scene
• DNA detected on sweat
band of cap
ProfilerPlus Blue Loci
Green Loci
ProfilerPlus Yellow Loci
Is defendant “included” as a possible
contributor to the DNA mixture on the cap?
D3
vWA
FGA
D8
Cap
14,15
(16)
15,16
(17)
24,25
(12)
[19.2, 23] 14,15
28,30,
(8) 11,
32.2[29] 12,13
(9,11)
12
Def.
14,15
16,16
19.2, 23
30,30
9,11
14,15
D21
D5
13,13
D13
Lab Report:
•There are three or more contributors to the mixture;
•Defendant is “included” as a possible contributor;
•Statistics offered on CPI (Cumulative probability of inclusion)
“Inclusion” is contingent on number of
contributors
D3
vWA
FGA
D8
D21
D5
Hat
14,15
(16)
15,16
(17)
24,25
[19.2,23]
(12)
14,15
28,30,
(8) 11,
32.2[29] 12,13
(9,11)
12
Def.
14,15
16,16
19.2,23
14,15
30,30
9,11
13,13
D13
•Defendant could be one of three or more contributors
•Defendant cannot be one of two contributors
•Can we rule out the possibility of two?
Defense Argument
• If there are three contributors, why are there
so few alleles (three or four per locus across
13 loci)
• The probability of seeing so few alleles is
higher IF there are two contributors than IF
there are three
• “If there are two, this case is through.”
Prosecution Response: Peak Height
Discrepancies Indicate Three Contributors
Defense Rejoinder: Peak
Height Discrepancies Are
Common
Unbalanced
alleles of 2
contributors—
NIST Mixture
Study #2
Balanced alleles
of same two
contributors
NIST Mixed Stain Study #2 (2 contributors)
Hat alleles (2 contributors?)
Result
• Six days of deliberation
• Jury deadlocked—mistrial
• Post-trial interviews
reveal…misunderstandings
Jurors’ conclusion: Five contributors
Likelihood Ratios
LR2 = p(E|Def & U1)/p(E|U1 & U2)
LR3 = p(E|Def & U1 & U2)/p(E|U1 & U2 & U3)
See, Biedermann, Taroni & Thompson, Law
Prob. & Risk 10, 89-121 (2011).
Sensitivity Analysis (Locus D21)
Architecture of Object-Oriented
Bayesian Network
Modeling of Peak Heights (Julia Mortera)
• “Extreme variability of peaks” makes mixture
difficult to explain under either model
• For 2 person mixture:
– Hp: Suspect and 1 unknown—1.77 x 10-108
– Hd: 2 unknowns—1.94 x 10-111
– LR=911
• For 3 person mixture
– Hp: Suspect and 2 unknowns—1.5 x 10-107
– Hd: 3 unknowns—5.5 x 10-111
– LR=2697
Whose priors?
• Parties (prosecution/defense)?
• Jurors?
• DNA expert?
Based on what?
• Observations on cap in question?
• General knowledge about caps?
• General knowledge about clothing worn by
criminals?
• Other evidence in the case?
Avoiding bias
• Should person estimating the prior be aware
of the consequences?
• What should that person be told about the
case?
Possible elicitation script
• A store clerk was shot and killed during a
robbery. Surveillance video revealed that
the shooter wore a white cap. The white
cap was found at the scene. It appeared to
be clean apart from some light staining on
the sweat band. It appeared to be relatively
new.
Possible elicitation script
• Suppose a DNA sample is found on the
sweat band of this cap. What is your best
estimate of the probability the sample
would contain alleles from:
–
–
–
–
–
One contributor only:
Two contributors:
Three contributors:
Four or more contributors:
Sum (Please make sure your
estimates sum to one)
_______
_______
_______
_______
_______
DNA Profile of Cap—ProfilerPlus Blue Loci
DNA Profile of Defendant
DNA Profile of Cap—ProfilerPlus Green Loci
Profile of Defendant
DNA Profile of Cap—ProfilerPlus Yellow Loci
Profile of Defendant