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