Page 1
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Workshop: Kinship analysisFirst lecture:
Basics: Genetics, weight of evidence. I.1
Thore Egeland(1),(2), Klaas Slooten(3),(4)
(1) Norwegian University of Life Sciences, (2) NIPH, (3) Netherlands ForensicInstitute, (4) VU University Amsterdam
Seoul, ISFG workshop, Aug 29 2017
1 / 25
Page 2
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Short bio
I Education:
Mathematics, statistics, computer science,mostly from University of Oslo.PhD in statistics, University of Oslo, 1989.
I Work:
Previously: Research, consulting.From 2011: Professor of statistics,Norwegian University of Life Sciences.20% position, Section of Forensics, Oslo University Hospital.
I Research interests:
Statistical, mathematical perspective on (forensic) genetics.Software: Familias (Windows and R).
I Norwegian: living in Oslo.
2 / 25
Page 3
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Contents of workshop
09:00-09:45 I.1 Basics: Genetics, weight of evidence (LR, Bayes). Thore.
09:45-10:30 I.2 Pairwise comparisons, IBD, mutation, theta,... Klaas.
10:30-11:30 Exercises. Coffee 11:00.
11:30-12:30 II LR properties. Interpretation. Klaas.
12:30-13:00 Exercises.
13:00-14:00 Lunch.
14:00-15:00 III.1 Familial searching, DVI. Klaas.
15:00-15:30 III.2 Mixtures and relatives. relMix demo. Thore.
15:30-16:00 Exercises.
16:00-16:30 IV.1,IV.2 Software: R. paramlink. Thore
16:30-17:45 Exercises.
17:45-18:00 Summary.
3 / 25
Page 4
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Contents 09:00–09:45
I Basic forensic genetics very briefly:
Mendelian inheritanceMarkers: autosomal, X, Y, mtDNA, STR-s.
I Weight of evidence. Likelihood Ratio (LR). Assumptions:
Hardy Weinberg Equilibrium (HWE).Linkage.Linkage disequilibrium (LD).
I Combining information. Bayes theorem:
Standard version.On odds form.On log form.
4 / 25
Page 5
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
5 / 25
Page 6
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Pedigree
6 / 25
Page 7
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Genetic markers I
7 / 25
Page 8
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Genetic markers II
8 / 25
Page 9
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
. Genetic markers III. Example: Fusion 6C
9 / 25
Page 10
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Mendelian inheritance
10 / 25
Page 11
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
X linked inheritance
11 / 25
Page 12
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Y linked inheritance
12 / 25
Page 13
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Mitochondrial (mtDNA) inheritance
13 / 25
Page 14
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Hypotheses
AF17/18
8/8
MO−/−−/−
CH17/17
8/8
I H1: AF biological father of CH.
I H2: AF and CH unrelated.
I Notation. Sometimes:
I H1 = HP :“prosecution hypothesis”,
I H2 = HD :“defence hypothesis”.
14 / 25
Page 15
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Likelihood ratio. Definition
Forensic framework
LR = LRH1,H2(E ) =P(E | H1)
P(E | H2)
is the likelihood ratio for evidence E with respect to the twohypotheses H1 and H2. The LR measures how much better H1
explains the evidence E than H2.
15 / 25
Page 16
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Likelihood Ratio. Example
AF17/18
8/8
MO−/−−/−
CH17/17
8/8
LR =P(E | H1)
P(E | H2)= · · · =
P(gCH | gAF )
P(gCH)
LR1 =12p17
p217=
1
2× 0.204= 2.45
LR2 =p8p28
=1
0.554= 1.81
LR = LR1 × LR2 = 2.45× 1.81 = 4.4.
16 / 25
Page 17
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Likelihood Ratio. Interpretation and assumptions
AF17/18
8/8
MO−/−−/−
CH17/17
8/8
I Interpretation LR=4.4: Thedata is 4.4 times more likelyif AF is assumed to be thefather compared to theunrelated alternative.
I Assumptions
Hardy–WeinbergEquilibrium (HWE).Independent markers.No artefacts:(no mutation, no silentalleles, no drop–out/in,no error).
17 / 25
Page 18
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Realistic number of markers
Marker CH AF LR LR(mut)
D3S1358 17/17 17/18 2.45 2.45TPOX 8/8 8/8 1.81 1.80
D6S474 16/17 14/15 0.000 0.001. . . . . . . . . . . . . . .
D19S433 12/15 12/14 3.34 3.34
Total 0 25070642
18 / 25
Page 19
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
W = Posterior probability of paternity
I Assume prior probabilities P(HP) = P(HD) = 0.5(reasonable?)
I Prior odds P(HP)P(HD)
= 1.
Then
W = P(HP | E ) =LR
LR + 1=
25070642
25070642 + 1
= 0.99999996 = ”Probability of HP given evidence”
19 / 25
Page 20
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Bayes theorem on odds form
20 / 25
Page 21
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Blackstone ratio
21 / 25
Page 22
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Optimal decision rule
22 / 25
Page 23
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Adding evidence I
23 / 25
Page 24
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
Adding evidence II
24 / 25
Page 25
Basic forensic geneticsWeight of evidence. Likelihood Ratio (LR)
Combining information. Bayes theorem
T Egeland, D Kling, and P Mostad.Relationship Inference with Familias and R: StatisticalMethods in Forensic Genetics.Academic Press, 2015.
A Tillmar and P Mostad.Choosing supplementary markers in forensic casework.Forensic Science International: Genetics, 13:128–133, 2014.
IJ Wood.Weight of evidence: A brief survey.Bayesian Statistics, 1985.
25 / 25