Transcript Using Bayesian Networks for Paternity Calculations: Adding

Bayesian Networks for the
Analysis of Evidence
Graphic and Visual Representations of Evidence
and Inference in Legal Settings
Cardozo School of Law
29 January 2007
A. Philip Dawid
Amanda B. Hepler
University College London
Outline
Wigmore Charts and Bayesian
Networks
Object Oriented Bayesian Networks
Sacco and Vanzetti case
Robbery Case
U Harold S. unlawfully and
intentionally assaulted and
injured a security guard
Willard R. during a break-in
at the Blackbread Brewery
premises, 27 Orchardson St.,
London NW8 in the early
morning hours of 1 May 2003
Wigmorean Analysis
U
P1
P2
P3
P4
Wigmorean Analysis
P1 In the early morning hours of 1 May, 2003, four
men unlawfully broke into the premises of the
Blackbread Brewery, located at 27 Orchardson St.,
London NW8
P2 Harold S. was one of the four men who broke
into the premises of the Blackbread Brewery in the
early morning hours of 1 May 2003
P3 A security guard at the Blackbread Brewery,
Willard R., was assaulted and injured during
the break-in
P4 It was Harold S. who intentionally assaulted
and injured Willard R. during the break-in
P2: Harold S. was one of the four men who broke into the premises of
the Blackbread Brewery in the early morning hours of 1 May, 2003
29)
30)
31)
32)
33)
34)
The intruders' car left immediately at the first sound of the alarm leaving the intruders stranded.
Willard R. testimony to 29).
The intruders dispersed from the Blackbread Brewery premises on foot.
Willard R. testimony to 31).
The four intruders went their separate ways.
In a search of the area surrounding the Blackbread Brewery premises, police apprehended Harold S. trying to "hot
wire" a car in an alley about 1/4 mile from the Blackbread Brewery premises.
35) DI Leary testimony to 34).
36) A photo of Harold S. taken shortly after his apprehension to be shown at trial.
37) The photo shown at trial is the same one police took of Harold R. shortly after his arrest.
38) The car Harold S. was trying to "hot wire" did not belong to him.
39) Harold S. was one of the four intruders fleeing the Blackbread Brewery premises.
40) During the police investigation a short time after the intrusion, the police found a tuft of red fibres on a jagged end
of one of the cut edges of the metal grille on the Blackbread premises.
41) DI Leary testimony to 40).
42) The tuft of fibres to be shown at trial.
43). The tuft of fibres shown at trial is the same one that police found on a jagged end of one of the cut edges of the
metal grille on the Blackbread premises.
44) The tuft of the fibres found on the metal grille on the Blackbread Brewery premises is red acrylic.
45) DI Leary testimony to 44).
46) The tuft of red acrylic fibres found on the metal grille came from an article of clothing.
47) The article of clothing the fibres came from was being worn at the time of the break-in at the Blackbread Brewery.
48) Harold S. was wearing a jumper and jeans at the time of his apprehension.
49) DI Leary testimony to 48).
50) The jumper and jeans to be shown at trial.
51) The jumper and jeans to be shown at trial are the same ones the police took from Harold S. after his apprehension.
52)
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54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
Harold S's jumper is made of red acrylic.
DI Leary testimony to 52).
Harold S. was wearing this red acrylic jumper at the time of the break-in at Blackbread Brewery.
The tuft of red fibres found on the metal grille on the Blackbread Brewery premises is visually indistinguishable
from the fibres on Harold S's jumper.
DI Leary testimony to 55)
The tuft of fibres and the jumper to be shown together at trial.
The tuft of fibres and the jumper are the same ones police obtained during their investigation of the break-in at the
Blackbread Brewery.
The tuft of red fibres found on the metal grille on the Blackbread Brewery premises is indistinguishable from the
fibres on Harold S's jumper as shown by a microspectroflourimetry analysis.
DI Leary testimony.
Microspectroflourimetry analysis result to be shown at trial.
The microspectroflourimetry results shown at trial are the same ones police obtained from the forensic scientist
["boffin"] who performed the analysis.
The tuft of red fibres found on the metal grille on the Blackbread Brewery premises is indistinguishable from the
fibres on Harold S's jumper as shown by a thin layer chromatography analysis.
DI Leary testimony to 63).
The results of the thin layer chromatography analysis.to be shown at trial.
The thin layer chromatography results shown at trial are the same ones police obtained from the forensic scientist
who performed the analysis.
The jumper belonging to Harold S. is well worn and has several holes in it.
DI Leary testimony to 67.
None of holes in Harold S's jumper can be clearly identified as a possible source of the tuft found on the metal grille
on the Blackbread Premises.
DI Leary testimony to 69).
Matches of tufts to holes in fabrics is very difficult.
The jumper worn by Harold S. on 1 May, 2003 was torn on a hole in the metal grille at the Blackbread premises.
Harold S. was wearing the article of clothing that produced the tuft of red acrylic found on a jagged end of the hole
cut into the metal grille at the Blackbread Brewery premises on 1 May, 2003.
Testimonial denial by Harold S. of P2, that he was one of four men who broke into the premises of the Blackbread
Brewery in the early morning hours of 1 May, 2003.
Wigmore Chart
P2: Harold S. was one of the four men who broke into the premises of
the Blackbread Brewery in the early morning hours of 1 May, 2003
P2
74
39
73
47
33
55
34
67
59
63
51
58
37
32
35
43
62
53
50
45
36
66
44
40
49
30
71
52
48
46
31
29
72
54
38
56
64
60
57
61
69
68
65
41
42
70
Bayesian Network
EYE WITNESS EVIDENCE
Guard’s evidence of no. of offenders
G1
Suspect guilty?
W
G2
Police evidence of arrest
Guard’s evidence of punch
C
N
No. of offenders
B
FIBRE EVIDENCE
Whose blood on jumper?
Jumper fibres
Suspect’s blood type Guard’s blood type
A
X3
X1
X2
Whose fibres on grille?
Y1
Grille fibres
R
Blood spray on jumper
Y2
BLOOD EVIDENCE
Jumper blood type
Commonalities of Wigmore Charts
and Bayesian Networks
Graphical inference networks
used to model many items of
evidence and their relationships
Represent individual standpoint
rather than “objective truth”
Support coherent narrative and
argumentation (?)
Differences
Wigmore Chart
Bayesian Network
• Tree-structured
• Created for evidence
in hand
• Nodes are events or
propositions
• Arrows indicate
inferential flow
• Qualitative analysis
and synthesis
• Symbolic distinctions
of type/effect of
evidence
• Directed Acyclic
Graph
• Created any time
• Nodes are variables
(any number of states)
• Arrows indicate
“causal” dependence
• Qualitative reasoning
about relevance
• Structural distinctions
of type/effect of
evidence
Sacco and Vanzetti Case
Sacco and Vanzetti Case
U Sacco and Vanzetti were
guilty of 1st degree murder
in the slaying of Berardelli
during the robbery that took
place in South Braintree, MA
on April 15, 1920
Sacco and Vanzetti Case
P1 Berardelli died of gunshot wounds he
received on April 15, 1920.
P2 At the time he was shot, Berardelli, along
with Parmenter, was in possession of a
payroll.
P3 It was Sacco who, with the assistance of
Vanzetti, intentionally fired shots that took
the life of Berardelli during a robbery of the
payroll he and Parmenter were carrying.
Bayesian Network
(Hugin 5)
P1
U
P2
P3
Some undesirable features
Large and messy
Complex modelling process
All evidence treated at same level
Hard to interpret
“Object-Oriented”
Bayesian Network
Level 1: 1st Degree Murder?
1st Degree Murder?
Berardelli
Murdered?
Felony
Committed?
Medical
evidence
Payroll robbery
evidence
P1
P2
Sacco is the
murderer?
P3
Level 2: Sacco is the Murderer?
P3
Opportunity?
Eyewitnesses
Alibi
Murder Car
Cap
Sacco is the
Murderer?
Firearms?
Motive?
Consciousness
of Guilt?
Level 3: Opportunity
Sacco at Scene?
Eyewitnesses?
Pelser
Constantino
Wade
Alibi?
Murder Car?
Sacco’s Cap
at Scene?
Level 4: Eyewitness Testimony
HUGIN 6
Sacco at Scene?
Similar to Sacco?
Pelser’s
Credibility
Wade’s
Credibility
Pelser’s
Testimony
Wade’s
Testimony
Level 4: Eyewitness Testimony
Eyewitnesses
HUGIN 6
Level 5: Generic Credibility
Generic Credibility
Eyewitnesses
Event
Competent?
Sensation?
Objectivity?
Veracity?
Testimony
HUGIN 6
Level 6: Attributes of Credibility
Generic Credibility
Eyewitnesses
Event
Competent?
Event
Sensation?
Objectivity?
Veracity?
Testimony
HUGIN 6
Sensation
Agreement?
Competent?
Sensation
Level 6: Attributes of Credibility
Generic Credibility
Eyewitnesses
Event
Competent?
Event
Sensation?
Objectivity?
Veracity?
Testimony
HUGIN 6
Sensation
Agreement?
Competent?
Sensation
Noisy Channel
In
Error?
Out
Level 4: Eyewitness Testimony
HUGIN 6
Sacco at Scene?
Similar to Sacco?
Pelser’s
Credibility
Wade’s
Credibility
Pelser’s
Testimony
Wade’s
Testimony
Level 4: Eyewitness Testimony
Eyewitnesses
HUGIN 6
Level 5: Specific Credibility
Evidence undercut by
ancillary evidence
Eyewitnesses
Event
Competent?
Generic
Credibility
Testimony
HUGIN 6
Constantino’s
Testimony
Other Generic Modules
Parent-Child
X
X
Y
Y
Probabilities
Boolean Case
X
True False
Y
True
p1
False 1-p1
1-p2
p2
p1
Generalization
(warrant)
p2
Statistical
Evidence
Expert Evidence
Identification
Item 1 = Item 2?
Attribute 1
...
Attribute N
Item 1 = Item 2?
Attribute
(Item 1)
Attribute
(Item 2)
Testimony
Testimony
“linked” evidence
Corroboration/Contradiction
2 or more sources giving
corroborative/ contradictory
statements about same event
Event
Credibility
Credibility
Source 1
Source 2
Convergence/Conflict
Testimony on 2 or more
compatible/ incompatible events
Hypothesis
Event 1
Event 2
Credibility
Credibility
Source 1
Source 2
Explaining Away
Knowledge of Cause 1 lowers probability
of Cause 2
Cause 1
Cause 2
Event
Wish List
Top-level display as Wigmore chart
Variable depth of display
Tailor generic class properties to
specific instance
Represent “causal” strength
Determine impact of evidence
Thank you!