Bayesian Networks for the

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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



Wigmore Charts and Bayesian
Networks


Object Oriented
Bayesian
Networks


Sacco and Vanzetti case


Outline

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 Case

P
1

U

P
2

P
3

P
4

Wigmorean Analysis

P
1

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


P
2

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


P
3

A security guard at the Blackbread Brewery,
Willard R.
, was

assaulted and injured
during
the break
-
in


P
4

It was

Harold S.
who
intentionally assaulted
and injured

Willard R. during the break
-
in

Wigmorean 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.

P
2
: 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 P
2
, 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.



29

30

31

32

33

34

35

36

37

38

39

42

41

40

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

P
2

74

73

72

P
2
: 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 Chart

Bayesian Network



B



Y
2

X
2

X
1





R

A

X
3





Y
1



C

G
2

W



N



G
1





BLOOD

EVIDENCE

FIBRE EVIDENCE

No. of offenders

Suspect’s blood type

Guard’s blood type

Jumper 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
and 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

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




Sacco and Vanzetti Case

U

Sacco

and Vanzetti were
guilty of

1
st

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

P
1


Berardelli
died of gunshot wounds

he
received on April 15, 1920.


P
2

At the time he was shot, Berardelli, along
with Parmenter, was
in possession of a
payroll
.


P
3


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 Case

Bayesian Network

(Hugin 5)

P1

P2

P3

U

Large and messy


Complex modelling process


All evidence treated at same level


Hard to interpret

“Object
-
Oriented”

Bayesian Network

Some undesirable features

Sacco is the


murderer?

1
st

Degree Murder?

Berardelli
Murdered?

Felony

Committed?

Medical

evidence

Payroll robbery
evidence

Level 1: 1
st

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?

P3

Sacco at Scene?

Sacco’s Cap

at Scene?

Alibi?

Eyewitnesses?

Pelser

Constantino

Wade

Murder Car?

Level 3: Opportunity

Level 4: Eyewitness Testimony

Similar to Sacco?

Pelser’s


Credibility

Pelser’s


Testimony

Wade’s


Credibility

Wade’s


Testimony

Sacco at Scene?

HUGIN 6

Level 4: Eyewitness Testimony

Eyewitnesses

HUGIN 6

Level 5: Generic Credibility

Eyewitnesses

Generic Credibility

Testimony

Competent?

Veracity?

Objectivity?

Sensation?

Event

HUGIN 6

Level 6: Attributes of Credibility

Eyewitnesses

Generic Credibility

Testimony

Competent?

Veracity?

Objectivity?

Sensation?

Event

Competent?

Sensation

Agreement?

Event

Sensation

HUGIN 6

Level 6: Attributes of Credibility

Eyewitnesses

Generic Credibility

Testimony

Competent?

Veracity?

Objectivity?

Sensation?

Event

Sensation

Noisy Channel

Out

In

Error?

Competent?

Sensation

Agreement?

Event

HUGIN 6

Level 4: Eyewitness Testimony

Similar to Sacco?

Pelser’s


Credibility

Pelser’s


Testimony

Wade’s


Credibility

Wade’s


Testimony

Sacco at Scene?

HUGIN 6

Level 4: Eyewitness Testimony

Eyewitnesses

HUGIN 6

Level 5: Specific Credibility

Eyewitnesses

Testimony

Event

Generic


Credibility

Competent?

Evidence undercut by
ancillary evidence

Constantino’s

Testimony

HUGIN 6

X

Parent
-
Child

Y

p
2

Generalization

(warrant)

p
1

X

True

False

Y

True

p
1

1
-
p
2

False

1
-
p
1

p
2

Boolean Case

Y

Probabilities

X

Statistical

Evidence

Expert Evidence

Other 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 chart

Variable depth of display

Tailor generic class properties to
specific instance


Represent “causal” strength

Determine impact of evidence


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