bayesian networks for the analysis of evidence graphic and visual representations of evidence and...
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Bayesian Networks for the Bayesian Networks for the Analysis of EvidenceAnalysis of Evidence
Graphic and Visual Representations of Evidence and Inference in Legal Settings
Cardozo School of Law29 January 2007
A. Philip Dawid Amanda B. Hepler
University College London
Wigmore Charts and Bayesian Networks
Object Oriented Bayesian Networks
Sacco and Vanzetti case
OutlineOutlineOutlineOutline
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
Robbery CaseRobbery CaseRobbery CaseRobbery Case
P1
U
P2 P3 P4
Wigmorean AnalysisWigmorean AnalysisWigmorean AnalysisWigmorean 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
Wigmorean AnalysisWigmorean AnalysisWigmorean AnalysisWigmorean Analysis
29) The intruders' car left immediately at the first sound of the alarm leaving the intruders stranded.30) Willard R. testimony to 29).31) The intruders dispersed from the Blackbread Brewery premises on foot.32) Willard R. testimony to 31).33) The four intruders went their separate ways. 34) 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.
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
52) Harold S's jumper is made of red acrylic.53) DI Leary testimony to 52). 54) Harold S. was wearing this red acrylic jumper at the time of the break-in at Blackbread Brewery.55) 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.56) DI Leary testimony to 55)57) The tuft of fibres and the jumper to be shown together at trial.58) The tuft of fibres and the jumper are the same ones police obtained during their investigation of the break-in at the
Blackbread Brewery.59) 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.60) DI Leary testimony.61) Microspectroflourimetry analysis result to be shown at trial.62) The microspectroflourimetry results shown at trial are the same ones police obtained from the forensic scientist
["boffin"] who performed the analysis.63) 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.64) DI Leary testimony to 63).65) The results of the thin layer chromatography analysis.to be shown at trial.66) The thin layer chromatography results shown at trial are the same ones police obtained from the forensic scientist
who performed the analysis.67) The jumper belonging to Harold S. is well worn and has several holes in it.68) DI Leary testimony to 67.69) 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.70) DI Leary testimony to 69).71) Matches of tufts to holes in fabrics is very difficult.72) The jumper worn by Harold S. on 1 May, 2003 was torn on a hole in the metal grille at the Blackbread premises.73) 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.
74) 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.
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P2
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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
Wigmore ChartWigmore ChartWigmore ChartWigmore Chart
Bayesian NetworkBayesian NetworkBayesian NetworkBayesian Network
B
Y2
X2X1 RAX3
Y1
C G2W N G1
BLOOD EVIDENCE
FIBRE EVIDENCE
No. of offenders
Suspect’s blood type Guard’s blood typeJumper fibres
Whose fibres on grille?
Grille fibres
Whose blood on jumper?
Guard’s evidence of no. of offenders Suspect guilty?
Blood spray on jumper
Jumper blood type
Police evidence of arrest
EYE WITNESS EVIDENCE
Guard’s evidence of punch
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 (?)
Commonalities of Wigmore Charts Commonalities of Wigmore Charts and Bayesian Networksand Bayesian Networks
Commonalities of Wigmore Charts Commonalities of Wigmore Charts and Bayesian Networksand Bayesian Networks
• 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
DifferencesDifferencesDifferencesDifferences
Wigmore Chart Bayesian Network
• 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 CaseSacco and Vanzetti CaseSacco and Vanzetti CaseSacco 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 CaseSacco and Vanzetti CaseSacco and Vanzetti CaseSacco 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.
Sacco and Vanzetti CaseSacco and Vanzetti CaseSacco and Vanzetti CaseSacco and Vanzetti Case
Bayesian NetworkBayesian Network(Hugin 5)(Hugin 5)
Bayesian NetworkBayesian Network(Hugin 5)(Hugin 5)
P1
P2
P3
U
Large and messy
Complex modelling process
All evidence treated at same level
Hard to interpret
““Object-Oriented”Object-Oriented”Bayesian NetworkBayesian Network““Object-Oriented”Object-Oriented”Bayesian NetworkBayesian Network
Some undesirable featuresSome undesirable featuresSome undesirable featuresSome undesirable features
Sacco is the murderer?
1st Degree Murder?
Berardelli Murdered?
Felony Committed?
Medical evidence
Payroll robbery evidence
Level 1: 1Level 1: 1stst Degree Murder? Degree Murder?Level 1: 1Level 1: 1stst Degree Murder? Degree Murder?
P1 P2
P3
Sacco is the Murderer?
Consciousness of Guilt?
Firearms?Opportunity?
Eyewitnesses
Cap
Murder Car
Alibi
Motive?
Level 2: Sacco is the Murderer?Level 2: Sacco is the Murderer?Level 2: Sacco is the Murderer?Level 2: Sacco is the Murderer?
P3
Sacco at Scene?
Sacco’s Cap at Scene?
Alibi?Eyewitnesses?
Pelser Constantino
Wade
Murder Car?
Level 3: OpportunityLevel 3: OpportunityLevel 3: OpportunityLevel 3: Opportunity
Level 4: Eyewitness TestimonyLevel 4: Eyewitness Testimony
Similar to Sacco?
Pelser’s Credibility
Pelser’s Testimony
Wade’s Credibility
Wade’s Testimony
Sacco at Scene?
HUGIN 6HUGIN 6
Level 4: Eyewitness TestimonyLevel 4: Eyewitness Testimony
Eyewitnesses
HUGIN 6HUGIN 6
Level 5: Generic CredibilityLevel 5: Generic Credibility
Eyewitnesses
Generic Credibility
Testimony
Competent?
Veracity?
Objectivity?
Sensation?
Event
HUGIN 6HUGIN 6
Level 6: Attributes of CredibilityLevel 6: Attributes of Credibility
Eyewitnesses
Generic Credibility
Testimony
Competent?
Veracity?
Objectivity?
Sensation?
Event
Competent?
Sensation
Agreement?
Event
Sensation
HUGIN 6HUGIN 6
Level 6: Attributes of CredibilityLevel 6: Attributes of Credibility
Eyewitnesses
Generic Credibility
Testimony
Competent?
Veracity?
Objectivity?
Sensation?
Event Sensation
Noisy Channel
Out
In Error?
Competent?
Sensation
Agreement?
Event
HUGIN 6HUGIN 6
Level 4: Eyewitness TestimonyLevel 4: Eyewitness Testimony
Similar to Sacco?
Pelser’s Credibility
Pelser’s Testimony
Wade’s Credibility
Wade’s Testimony
Sacco at Scene?
HUGIN 6HUGIN 6
Level 4: Eyewitness TestimonyLevel 4: Eyewitness Testimony
Eyewitnesses
HUGIN 6HUGIN 6
Level 5: Specific CredibilityLevel 5: Specific Credibility
Eyewitnesses
Testimony
Event
Generic Credibility
Competent?
Evidence undercut by ancillary evidence
Constantino’s Testimony
HUGIN 6HUGIN 6
XParent-Child
Y
p2
Generalization(warrant)
p1
X
True False
YTrue p1 1-p2
False 1-p1 p2
Boolean Case
Y Probabilities
X
Statistical Evidence
Expert Evidence
Other Generic ModulesOther Generic ModulesOther Generic ModulesOther Generic Modules
Item 1 = Item 2?
Attribute 1 ... Attribute N
Item 1 = Item 2?
Testimony
Attribute (Item 1)
Testimony
Attribute(Item 2)
Identification
“linked” evidence
2 or more sources giving corroborative/ contradictory statements about same event
Event
Credibility Credibility
Source 1 Source 2
Corroboration/ Contradiction
Testimony on 2 or more compatible/ incompatible events
Hypothesis
Credibility Credibility
Source 1 Source 2
Event 1 Event 2
Convergence/Conflict
Knowledge of Cause 1 lowers probability of Cause 2
Event
Cause 1 Cause 2
Explaining Away
Top-level display as Wigmore chartVariable depth of display Tailor generic class properties to specific instance
Represent “causal” strengthDetermine impact of evidence
Wish ListWish ListWish ListWish List
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