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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

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bayesian networks for the analysis of evidence

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
Outline
  • Wigmore Charts and Bayesian Networks
  • Object Oriented Bayesian Networks
  • Sacco and Vanzetti case
slide3

Robbery Case

UHarold S.unlawfully and intentionallyassaultedand injured a security guardWillard R.during abreak-inat the Blackbread Brewery premises, 27 Orchardson St., London NW8 in the early morning hours of 1 May 2003

slide4

U

P1

P2

P4

P3

Wigmorean Analysis

slide5

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

P2Harold 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., wasassaulted and injured during the break-in

P4 It was Harold S. who intentionally assaulted and injured Willard R. during the break-in

slide6

P2: Harold S. was one of the four men who broke into the premises of the BlackbreadBrewery in the early morning hours of 1 May, 2003

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.

slide7
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.

slide8

P2

74

73

39

47

72

54

71

33

38

52

48

67

46

31

55

59

29

63

34

66

51

58

62

44

37

40

49

53

69

64

56

68

30

32

35

60

43

50

65

61

45

57

41

36

42

70

Wigmore Chart

P2: Harold S. was one of the four men who broke into the premises of the BlackbreadBrewery in the early morning hours of 1 May, 2003

bayesian network

EYE WITNESS EVIDENCE

Guard’s evidence of no. of offenders

Suspect guilty?

G2

W

C

G1

N

Police evidence of arrest

No. of offenders

Guard’s evidence of punch

B

FIBRE EVIDENCE

Whose blood on jumper?

Jumper fibres

Guard’s blood type

Suspect’s blood type

R

A

X3

X1

X2

Whose fibres on grille?

Blood spray on jumper

Y2

BLOODEVIDENCE

Y1

Jumper blood type

Grille fibres

Bayesian Network
slide10

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 (?)
slide11

Differences

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
  • 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
sacco and vanzetti case13
Sacco and Vanzetti Case

USaccoand Vanzetti were guilty of1st degree murderin the slaying ofBerardelli during therobberythat took place in South Braintree, MA on April 15, 1920

sacco and vanzetti case14
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.

slide16

“Object-Oriented”Bayesian Network

Some undesirable features

  • Large and messy
  • Complex modelling process
  • All evidence treated at same level
  • Hard to interpret
slide17

Payroll robbery evidence

Level 1: 1st Degree Murder?

1st Degree Murder?

Sacco is the murderer?

Felony Committed?

Berardelli Murdered?

P3

Medical evidence

P2

P1

slide18

Opportunity?

Eyewitnesses

Alibi

Murder Car

Cap

Level 2: Sacco is the Murderer?

Sacco is the Murderer?

P3

Consciousness of Guilt?

Firearms?

Motive?

slide19

Eyewitnesses?

Pelser Constantino

Wade

Level 3: Opportunity

Sacco at Scene?

Sacco’s Cap at Scene?

Alibi?

Murder Car?

level 4 eyewitness testimony
Level 4: Eyewitness Testimony

Sacco at Scene?

Similar to Sacco?

Pelser’s Credibility

Wade’s Credibility

Pelser’s Testimony

Wade’s Testimony

HUGIN 6

level 5 generic credibility
Level 5: Generic Credibility

Generic Credibility

Event

Competent?

Eyewitnesses

Sensation?

Objectivity?

Veracity?

Testimony

HUGIN 6

level 6 attributes of credibility

Event

Agreement?

Competent?

Sensation

Level 6: Attributes of Credibility

Generic Credibility

Sensation

Event

Competent?

Eyewitnesses

Sensation?

Objectivity?

Veracity?

Testimony

HUGIN 6

level 6 attributes of credibility24

Event

Agreement?

Competent?

Sensation

In

Error?

Out

Level 6: Attributes of Credibility

Generic Credibility

Sensation

Event

Competent?

Eyewitnesses

Sensation?

Objectivity?

Veracity?

Noisy Channel

Testimony

HUGIN 6

level 4 eyewitness testimony25
Level 4: Eyewitness Testimony

Sacco at Scene?

Similar to Sacco?

Pelser’s Credibility

Wade’s Credibility

Pelser’s Testimony

Wade’s Testimony

HUGIN 6

level 5 specific credibility

Evidence undercut by ancillary evidence

Constantino’s Testimony

Level 5: Specific Credibility

Eyewitnesses

Event

Competent?

Generic Credibility

Testimony

HUGIN 6

slide28

X

Probabilities

Y

Generalization

(warrant)

p1

p2

Statistical Evidence

Expert Evidence

Other Generic Modules

Parent-Child

X

Y

Boolean Case

slide29

Item 1 = Item 2?

Attribute(Item 2)

Attribute (Item 1)

Testimony

Testimony

Identification

Item 1 = Item 2?

...

Attribute N

Attribute 1

“linked” evidence

slide30

2 or more sources giving corroborative/ contradictory statementsabout same event

Event

Credibility

Credibility

Source 1

Source 2

slide31

Convergence/Conflict

Testimony on 2 or more compatible/ incompatible events

Hypothesis

Event 1

Event 2

Credibility

Credibility

Source 1

Source 2

slide32

Explaining Away

Knowledge of Cause 1 lowers probability of Cause 2

Cause 1

Cause 2

Event

slide33

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