-
A Abby 32.6% +/-unk #1 56.3% +/-unk #2 the rest
Likelihood of observed mixturecase 2015:0095 M 4SL
proportion from A Abbypro
portio
n from
unk #
1
log
Like
lihoo
d
0%
17%
33%
42% 39%
44% 50%
56% 63%
68%-65
-64
-63
-62
-61
A Abby 27.0% +/-O Oscar 41.1% +/-unk #1 the rest
Likelihood of observed mixturecase 2015:0095 M 4SL
proportion from A Abbypro
portio
n from
O O
scar
log
Like
lihoo
d
0% 8%
17%
27%
35%
42% 13%
22% 31%
41% 50%
60%-65
-64
-63
-62
-61
The DNA·VIEW® Mixture Solution CH Brenner, DNA·VIEW & Human Rights Center, UC Berkeley
References Evaluating forensic DNA profiles using peak heights, allowing for multiple donors, allelic dropout and stutters,
Roberto Puch-Solis, Lauren Rodgers, Anjali Mazumder, Susan Pope, Ian Evett, James Curran, David Balding, Forensic Science International: Genetics 7 (2013) 555–563
Computational aspects of DNA mixture analysis / Exact inference using auxiliary variables in a Bayesian network, Therese Graversen &Steffen Lauritzen, Stat Comput DOI 10.1007/s11222-014-9451-7
Continuous-model mixture analysis Mixture Solution™ is a computer program for solving mixture problems by a “continuous” approach – that is, the calculation takes into account the significance of peak height including varying contribution amounts along with random peak height variation. • Visual aids – answer “black box” concern. • Coherent simple model for likelihood
computations – based mainly on stochastic variation,
incorporates dropout, drop-in, stutter and allelic stacking naturally and without additional “moving parts.”
– Robust: not sensitive to exact parameter values
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
PHR
Expected RFU
(typical, 3130) Stochastic Variation Modelexpected Peak Height Ratio
90th %ile68th %ileMedian peak height ratio32nd %ile10th %ile
Mixture L as ABCZ+0 unknowns Maximum likelihood proportions:
LR=
Stochastic variation (follows gamma distribution)
moderate misfit penalty
“Casework model” (of Mixture Solution) • Multiple potential contributors S, T, U, … • May be 2-person, may be 3-person … mixture • Explore automatically all Hp-Hd combinations
• Find best Hp & best Hd, & LR
Continuous evaluation model • LR for Hp vs Hd • Stochastic behavior • Dropout, dropin, stutter, …
Hp=prosecution hypothesis
Hd=defense hypothesis
LR=evidence for Hp vs Hd
Defense hypotheses . A&2unk A&3unk O&2unk O&3unk O&1unk A&1unk
Pros
ecut
ion
hypo
thes
es
AO&2unk LR=190 vs O 225 LR=660 vs A 1000 2E+13 8E+13 AO&3unk 94 110 330 510 1E+13 4E+13 AO&1unk 10 13 38 60 1E+12 4E+12 AO&0unk 0 0 0 0 0 0
Best hypotheses to: defend A defend O prosecute
0
10
20
30
AO A O
3 2 1 0
reference contributors
# of unknown contributors
Computation
seconds
65 seconds total time 10 hypotheses
Explore & Solve • Explores many hypotheses • Decides appropriate # of unknown
contributors • Evaluates many different combinations
of references as contributors • Uses mathematics, not MCMC
#348 ISFG2015
90x120
Strength of evidence (Likelihood Ratios)
Slide Number 1