Object Oriented Bayesian Networks for the Analysis of Evidence

1
Object Oriented Bayesian Networks for the
Analysis of Evidence

• Joint Seminar
• Dept. of Statistical Science
• Evidence Inference Enquiry Programme
• 5 February 2007
• A. Philip Dawid
• Amanda B. Hepler

2
Outline

• Introduction to Wigmore Charts
• Illustration (S V Case)
• Introduction to Bayesian networks
• Illustration (S V Case)
• Comparison
• Best of both worldsOOBN Illustration

3
Wigmore Chart Method

• Analysis
• Define the ultimate and penultimate probanda
• Identify relevant items of evidence (trifles)
• Assign trifles to penultimate probanda
• Synthesis
• Constructing key lists bearing upon probanda
• Draw a chart showing the inferential linkages
  among the elements of the key list

4
Example Probanda

• Ultimate Probandum
• 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.
• Penultimate Probanda
• Berardelli died of gunshot wounds.
• When he was shot, Berardelli was in possession
  of a payroll.
• Sacco intentionally fired shots that killed
  Berardelli.

U
Kadane, J. B. and Schum, D. A. (1996). A
probabilistic analysis of the Sacco and
Vanzetti evidence. Wiley.
5
Example Key List

•  
• A bullet was removed from Parmenter sometime
  after 400 pm on April 15, 1920 this bullet
  perforated his vena cava.
• Dr. Hunting testimony to 1.
• Parmenter died at 500 am on April 16, 1990.
• Anonymous witness testimony to 3.
• Berardelli died at 400 pm on April 15, 1920.
• Dr. Fraser testimony to 5.
• Four bullets were extracted from Berardellis
  body. Dr. Magrath labelled the lethal bullet as
  bullet III the other three were marked I, II,
  and IV.
• Dr. Magrath testimony to 6.
• The Slater Morrill payroll was delivered to
  Hampton House on the morning of April 15, 1920.
• S. Neal testimony to 9.
• .
• .
• .
• Sacco lied about his Colt and cartridges, during
  inquiry, to protect his friends in the anarchist
  movement.
• Sacco testimony to 477.
• Saccos lies about his Colt had nothing to do
  with his radical friends.
• Sacco admission on cross-examination

6
Example Abbreviated Wigmore Chart
U

P3
P1
P2
11
13
1
3
5
18
59
67
82
156
358
7
14
2
4
6
8
9
12
Charts 3 6
Chart 14
Chart 25
10
15
17
16
Charts 15, 16, 17, 21, 22
Charts 19 22
Charts 7 8

• Complete Wigmore charts are located in Appendix
  A of Kadane and Schum.

7
Observations on Wigmorean Analysis

• A graphical display organizing masses of
  evidence.
• Events and hypotheses must be represented as
  binary propositions.
• Intended to model argument strategies for both
  sides of a case.
• Arrows indicate inferential flow.
• Designed for qualitative analysis, although
  likelihood calculations can easily be derived
  (see Kadane and Schum).

8
Bayesian Network Method

• Analysis
• Define unknown variables to be represented as
  nodes in the network.
• Identify relevant items of evidential facts to
  also become nodes in network.
• Determine any probabilistic dependencies.
• Synthesis
• Create nodes (unknown variables evidentiary
  facts).
• Connect nodes using arrows representing
  probabilistic dependence.

9
Example Abbreviated Bayes Net(Hugin)
10
Observations on Bayesian Networks

• Graphical display organizing masses of evidence
• Events and hypotheses can be represented with any
  number of states
• Intended to model probabilistic relationships
  among variables
• Arrows indicate causal flow
• Designed for quantitative analysis, and
  likelihood calculations are automatic

11
Some Desirable Features

• Can handle complex cases with masses of evidence.
  (BN WC)
• Likelihoods can quantify probative force of the
  evidence. (BN)
• Conditional probability tables can guide thinking
  when unclear about dependencies. (BN)
• Listing probanda and trifles can guide thinking
  when unclear of relevant items to consider. (WC)

12
Some Undesirable Features (BN WC)

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

13
Recall Wigmorean Analysis

• 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
• Berardelli died of gunshot wounds
• When he was shot, Berardelli was in possession
  of a payroll.
• Sacco intentionally fired shots that killed
  Berardelli during a robbery of the payroll.

U
P1
P2
P3
14
Level 1 1st Degree Murder?
U
1st Degree Murder?
Sacco is the murderer?
Felony Committed?
Berardelli Murdered?
P3
Medical evidence
P2
P1
15
Level 2 Sacco is the Murderer?
P3
Sacco is the Murderer?
Consciousness of Guilt?
Firearms?
Motive?
16
Level 3 Opportunity
Sacco at Scene?
Saccos Cap at Scene?
Alibi?
Murder Car?
17
Level 4 Eyewitness Testimony
Similar to Sacco?
Sacco at Scene?
Pelsers Credibility
Wades Credibility
Pelsers Testimony
Wades Testimony
18
Level 5 Generic Credibility
Generic Credibility
Competent?
Event
Eyewitnesses
Sensation?
Objectivity?
Veracity?
Testimony
19
Level 6 Attributes of Credibility
Generic Credibility
Sensation
Competent?
Event
Eyewitnesses
Sensation?
Objectivity?
Veracity?
Testimony
20
Level 6 Attributes of Credibility
Generic Credibility
Sensation
Competent?
Event
Eyewitnesses
Sensation?
Objectivity?
Veracity?
Noisy Channel
Testimony
21
Level 4 Eyewitness Testimony
Similar to Sacco?
Sacco at Scene?
Pelsers Credibility
Wades Credibility
Pelsers Testimony
Wades Testimony
22
Level 5 Specific Credibility
Eyewitnesses
Event
Competent?
Generic Credibility
Testimony
23
Level 1 1st Degree Murder?
U
1st Degree Murder?
Sacco is the murderer?
Felony Committed?
Berardelli Murdered?
P3
Medical evidence
P2
P1
24
Other Generic Modules, so far

• Identification (DNA, Saccos cap)
• Corroboration/Contradiction
• 2 or more sources giving the same or differing
  statements about the same event
• Convergence/Conflict
• Testimony by 2 or more events that lead to the
  same or differing conclusions about a hypothesis
• Explaining Away
• Knowledge of one cause lowers probability of
  another cause

25
Demystifying the Numbers
X
Parent-Child
Y
Boolean Case
26
Software Limitations

• Need a program to streamline the process,
  incorporating concepts from both WC BN
• Hierarchical displays in HUGIN are lacking
• Drag and drop from text (i.e. Rationale,
  Araucaria)
• Would like probabilities to be randomly drawn
  from a distribution, facilitating sensitivity
  analysis
• HUGIN runtime is slow for large oobns (10 nested
  networks)

27
Thank you!