Bayesian Networks for the Analysis of Evidence

1. 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

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

3. 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

4. U P1 P2 P4 P3 Wigmorean Analysis

5. 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

6. 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.

7. 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.

8. 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

9. 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

10. 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 (?)

11. 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

12. Sacco and Vanzetti Case

13. 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

14. 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.

15. Bayesian Network(Hugin 5) U P1 P2 P3

16. “Object-Oriented”Bayesian Network Some undesirable features • Large and messy • Complex modelling process • All evidence treated at same level • Hard to interpret

17. Payroll robbery evidence Level 1: 1st Degree Murder? 1st Degree Murder? Sacco is the murderer? Felony Committed? Berardelli Murdered? P3 Medical evidence P2 P1

18. Opportunity? Eyewitnesses Alibi Murder Car Cap Level 2: Sacco is the Murderer? Sacco is the Murderer? P3 Consciousness of Guilt? Firearms? Motive?

19. Eyewitnesses? Pelser Constantino Wade Level 3: Opportunity Sacco at Scene? Sacco’s Cap at Scene? Alibi? Murder Car?

20. Level 4: Eyewitness Testimony Sacco at Scene? Similar to Sacco? Pelser’s Credibility Wade’s Credibility Pelser’s Testimony Wade’s Testimony HUGIN 6

21. Level 4: Eyewitness Testimony Eyewitnesses HUGIN 6

22. Level 5: Generic Credibility Generic Credibility Event Competent? Eyewitnesses Sensation? Objectivity? Veracity? Testimony HUGIN 6

23. Event Agreement? Competent? Sensation Level 6: Attributes of Credibility Generic Credibility Sensation Event Competent? Eyewitnesses Sensation? Objectivity? Veracity? Testimony HUGIN 6

24. 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

25. Level 4: Eyewitness Testimony Sacco at Scene? Similar to Sacco? Pelser’s Credibility Wade’s Credibility Pelser’s Testimony Wade’s Testimony HUGIN 6

26. Level 4: Eyewitness Testimony Eyewitnesses HUGIN 6

27. Evidence undercut by ancillary evidence Constantino’s Testimony Level 5: Specific Credibility Eyewitnesses Event Competent? Generic Credibility Testimony HUGIN 6

28. X Probabilities Y Generalization (warrant) p1 p2 Statistical Evidence Expert Evidence Other Generic Modules Parent-Child X Y Boolean Case

29. Item 1 = Item 2? Attribute(Item 2) Attribute (Item 1) Testimony Testimony Identification Item 1 = Item 2? ... Attribute N Attribute 1 “linked” evidence

30. 2 or more sources giving corroborative/ contradictory statementsabout same event Event Credibility Credibility Source 1 Source 2

31. Convergence/Conflict Testimony on 2 or more compatible/ incompatible events Hypothesis Event 1 Event 2 Credibility Credibility Source 1 Source 2

32. Explaining Away Knowledge of Cause 1 lowers probability of Cause 2 Cause 1 Cause 2 Event

33. 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

34. Thank you!