UNIVERSITY COLLEGE LONDON
STUDIES OF EVIDENCE SCIENCE
A WIGMOREAN INTERPRETATION OF
THE EVALUATION OF A COMPLICATED
PATTERN OF EVIDENCE
David A. Schum*
School of Information Technology & Engineering
School of Law
George Mason University
Honorary Professor of Evidence Science
University College London
4 February, 2005
[Revised]
* The author is most grateful to the Leverhulme Foundation and the Economic and Social
Research Council for their support of the research described in this paper.
1.0 INTRODUCTORY COMMENTS
An important part of our studies of the science of evidence involves examining alternative
methods for analyzing complex probabilistic situations in which we often have a large mass of
evidence to evaluate. The structuring of complex arguments based on a mass of evidence can be
done in different ways to suit the interests of persons having different standpoints, as I noted in a
recent paper1. The present paper concerns a complex pattern of evidence that can be analyzed
in different ways. The example I am using in this paper comes from a hypothetical criminal law
case employed in a recent paper Professors Dawid and Evett have written to illustrate graphical
Bayesian methods for evaluating complicated patterns of evidence2. The methods described in
this paper are also called Probabilistic Expert Systems [PES]. The PES described by Dawid and
Evett is based on first constructing a directed acyclic graph [DAG] whose structure represents
what is believed to be a plausible pattern of linkages among probabilistic variables, each
representing an element of concern in the analysis at hand. The DAG constructed by Dawid and
Evett in their analysis of the hypothetical case is what I have called a "process model" 3, since it is
intended to capture a complex process by which some series of events could have been
generated in the case being analyzed. The DAG contrived by Dawid and Evett, and that I will
examine in my analysis, is several orders of magnitude more interesting and complex than the toy
problems so often used to illustrate Bayesian networks. Actual probabilistic analyses of this DAG
could have made use of any one of the existing software systems such as HUGIN, NETICA, or
ERGO to perform Bayesian analyses of this inference network or process model.
In my present analysis I have taken the very same evidence upon which the Dawid/Evett
example is based. But the inference network I have constructed is based on a different standpoint
than the one they adopted. I have tarted up the criminal law case example by including some
fictitious names, places, and times. I have done this because it will make my analysis more easy
to follow. But I have not changed any of the evidence used by Dawid and Evett. To make this
paper informal, and also to save space, Professor Dawid is "Phil" and Professor Schum is "Dave"
in the following discussion..
2.0 STANDPOINT MATTERS
William Twining is quite correct in urging all of us to declare our standpoints, up front, in
any kind of analysis. So, here comes my attempt to declare a standpoint for Phil's analysis of the
example case at hand and for me in my different analysis of this same example. I hope Phil
agrees with the standpoint I have declared for him.
2.1 Phil's Standpoint
In answer to the first standpoint question, Who am I? [i.e. What Hat am I wearing?], I
declare Phil to be a world renowned probabilist/statistician with an interest in developing methods
for analyzing complex masses of evidence. The second standpoint question is: At what stage of
what process am I?. The process in which Phil is involved seems to be research and instruction
involving Bayesian methods for the analysis of inference networks based on masses of evidence
whose items have a variety of subtle and interesting properties. I am not too sure how to declare
what stage of this process Phil is in. As far as research is concerned, I can't say that Phil is in the
beginning stages of this process since work on Bayes's nets has been going on for quite some
time now. So I'll just say that Phil is in the process of advancing research on Bayesian inference
networks. As far as instruction is concerned, I guess I can say that Phil is in the fairly early stages
of the process of trying to educate persons in the forensic sciences about the virtues of graphical
1
Schum, D. Alternative Views of Argument Construction from a Mass of Evidence. Cardozo Law
Review, Vol. 22, Nos. 5-6, July, 2002, pp 1461 - 1502.
2 Dawid, P., Evett, I. Using a Graphical Method to Assist the Evaluation of Complicated Patterns
of Evidence. Journal of Forensic Sciences, March 1997, pp 226 - 231.
3 See note 1 at pages 1466 - 1468.
2
Bayesian analyses. The final standpoint question is: What are my objectives? In the abstract of
the Dawid/Evett paper the authors declare the objective of their analysis is to show persons in the
forensic sciences how probabilistic expert systems can assist in the interpretation of evidence in
situations in which there are complex dependency relations between different aspects of the
evidence being considered.
2.2 Dave's Standpoint
Who am I? [i.e. What Hat am I wearing?}. In my analysis I am adopting the role of a
prosecuting attorney who is trained in Wigmorean analysis of complex masses of evidence. This
attorney has studied under Professor William Twining and he has read Twining's book with
Professor Terry Anderson from cover to cover4. At what stage of what process am I? Fact
investigation in the case at hand is not yet complete but I am in the act of preparing a case
against the defendant, later named. I believe I know what crime this defendant should be charged
with although I might have to change my mind pending other evidence that might be gathered. I
am in the early stages of constructing defensible and persuasive arguments in defense of the
relevance of the evidence we have so far on an ultimate probandum [matter to be proved] that is
given below. Third, my objective is to prepare a case for presentation in a criminal court that will
show, beyond reasonable doubt, that the defendant committed the crime with which he is
charged.
3.0 SOME PRELIMINARIES
A standard Wigmorean analysis in criminal affairs, such as the one in Phil's example,
always assumes the existence of an ultimate probandum [a matter to be proved] and a collection
of penultimate probanda, each of which must be shown true beyond reasonable doubt in order to
prove the ultimate probandum beyond reasonable doubt. The penultimate probanda for any
specific charge specified in an ultimate probandum are given by substantive law. In most cases
the penultimate probanda result from a parsing of an ultimate probandum into specific elements
that form a necessary and sufficient basis for proving the ultimate probandum. As Anderson and
Twining tell us, these penultimate probanda provide the touchstones for determining the
relevance of any item of evidence to be admitted at trial. In other words, these penultimate
probanda provide the necessary relevance "hooks" on which all of the trial evidence must be
hung. In describing what are the ultimate and penultimate probanda in the example being
analyzed, I now give some fictitious names, places and dates in the criminal law example. The
commercial premises in which the alleged intruders entered belong to the Blackbread Brewery,
located at 27 Orchardson St. London N.W. 8. The defendant in this case is Harold S., an
unemployed hotel porter whose stated address is: 12 Widley Rd., London, W. 9. The security
guard victim in this case is Willard R., whose stated address is: 34 Samford St., London N. W. 8.
To simplify the police testimony in this case, I will assume that it is to be given by just one person,
none other than Detective Inspector Richard Leary [I hope Richard will not mind being demoted in
this example. I could not see him, as Detective Chief Inspector, riding around in a patrol car].
3.1 Ultimate and Penultimate Probanda in My Analysis
I first had to generate an ultimate probandum that seems appropriate in Phil's example
that I am about to analyze in Wigmorean terms. On the evidence we have, it seems that the
defendant Harold S. was involved in two felonies: a break-in and an assault leading to an injury.
In former times, what we now call a break-in used to be described as breaking and entering.
There are two elements of the charge of break-in. It must have been illegal or unauthorized, and it
must have been forced. The four intruders may have had objectives other than just a break-in,
such as burglary or some form of malicious destruction. But, as prosecutor I don't have any
4
Anderson, T., Twining, W. The Analysis of Evidence: How to Do Things with Facts Based on
Wigmore's Science of Judicial Proof. Northwestern University Press, 1998.
3
evidence regarding their intentions. So, I will entertain a charge specified in the following ultimate
probandum:
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 N.
W. 8 in the early morning hours of 1 May, 2003.
Here's my collection of penultimate probanda associated with U above. I am assuming that these
penultimate probanda would correspond to what is required by English law. [William Twining can
correct me if I am wrong].
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 N. W. 8.
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 at the Blackbread Brewery on 1 May, 2003.
P4: It was Harold S. who intentionally assaulted and injured Willard R. during the break-in
at Blackbread Brewery on 1 May, 2003.
With this given U and the four penultimate probanda now specified, I can provide the topmost part of my Wigmorean argument structure for the example being considered.
U
P1
P2
P3
P4
To be relevant in this fictitious case, all of the evidence items must be linked, by argument, to one
of the four penultimate probanda shown above. An exception concerns any evidence items that
are taken as being ancillary evidence. We will have a few items of ancillary evidence.
3.2 Parsing Evidence into Details or "Trifles"
At several points in their investigative work, Sherlock Holmes tells Dr. Watson: "You know
my method. It is based on the observance of trifles". Trifles refer to any individual details obtained
from tangible or testimonial evidence obtained during an investigation of any kind. A tangible
object may reveal any number of trifles or details. Similarly, testimony of a witness may, when
parsed, reveal any number of trifles. Some trifles turn out to be inferentially important in various
ways while other trifles are unimportant. It should be noted here that there's an element of
subjectivity in the parsing of any item of potential evidence. Different persons might identify
different trifles in any item of incoming information. What gets charted as evidence in any
Wigmorean analysis are individual trifles or details. To be relevant and become evidence a trifle
must be linked, directly or indirectly, to one of the four penultimate probanda listed above. There
are several reasons for the necessity of parsing or decomposing our observations of any kind into
individual trifles. First, consider an item of testimony in which a witness asserts trifles A, B, and C.
This witness's credibility in asserting A we might believe to be less than it is in his/her assertion of
trifles B and C. Second, trifles A and B might be relevant on one penultimate probandum, while
4
trifle C might be relevant on a different penultimate probandum. Third, in ordinary Wigmorean
analyses in legal applications we commonly concern ourselves with binary propositions that can
in principle be shown to be true or false. Suppose a witness asserts trifle E*, that event E
occurred. Just because we have testimony E* does not entail that event E did occur. So our
inference from E* concerns events in the binary class {E, E c}. Did E occur or not [Ec]? Sources of
doubt, interposed between our evidential trifles and penultimate probanda, are also usually stated
as binary propositions that can be shown true or false. These propositions, along with the ultimate
and penultimate probanda in a Wigmorean analysis, correspond to the probabilistic variables in
conventional Bayesian network analyses.
I mentioned earlier that Phil's example we are now considering is considerably more
complex than others usually constructed to illustrate the workings and virtues of Bayesian
analyses. In my parsing of Phil's example, I have identified 30 trifles which I list below. But, as
you will see, the following listing contains more than 30 items that might become relevant
evidence if you buy my arguments linking them to one of the four penultimate probanda listed
above. The reason is that we might obtain more than one kind of evidence regarding certain
trifles. For example, DI Leary will testify to the existence of the hole cut in the metal grille at the
Blackbread premises [this will justify my claim that the break-in was forced]. To corroborate this
testimony, Leary would then offer a photograph showing the hole in this metal grille. There will be
several instances of my including this kind of corroboration. I am not making up any new
evidence here; I am just showing how the same evidence might be presented in more than one
way. As the prosecutor in this case, I must try to corroborate testimonial assertions whenever I
can.
3.3 Trifles in Phil's Example
Here are the thirty trifles that I have identified in Phil's example. Along with each trifle, I
mention the source from which it comes. Again, note that we may have corroborations of items of
testimonial evidence, so the number of potential evidence items to be charted will be greater than
thirty.
1. An unknown number of persons entered the commercial premises of the Blackbread
Brewery in the early morning hours of 1 May, 2003. DI Leary testimony.
2. The persons entered the premises of the Blackbread Brewery by means of a hole
that they cut in a metal grille. DI Leary testimony plus a photo showing the hole.
3. After entering the Blackbread premises the intruders were confronted by a security
guard named Willard R. Willard R testimony.
4. Upon seeing the intruders, the security guard set off an alarm. Willard R. testimony.
5. After he set off the alarm, the security guard Willard R. was punched in the face by
one of the intruders. Willard R. testimony.
6. The punch Willard R. received from one of the intruders caused Willard R's nose to
bleed. Willard R. testimony plus a photo of his injury taken shortly after the incident.
7. The intruders left the Blackbread premises just as a police patrol car arrived. Willard
R. testimony.
8. The intruders' getaway car left immediately at the first sound of the alarm leaving the
intruders stranded. Willard R. testimony.
9. The intruders dispersed from the Blackbread premises on foot. Willard R. testimony.
10. There were four intruders. Willard R. testimony.
11. The security guard could not describe the intruders. Willard R. testimony.
12. The light was poor at the time of the intrusion. Willard R. testimony.
13. The security guard was confused because of the blow he had received. Willard R.
testimony.
14. The police in the patrol car that had arrived at the Blackbread premises saw the
intruders from a considerable distance away. DI Leary testimony.
15. In a search of the area surrounding the Blackbread premises, police apprehended
Harold S. trying to "hot wire" a car in an ally about 1/4 mile from the Blackbread
5
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
premises. DI Leary testimony plus a photo of Harold S. taken just after he was
apprehended.
During a police investigation a short time after the intrusion, a tuft of red fibres was
found on a jagged end of one of the cut edges of the metal grille on the Blackbread
premises. DI Leary testimony plus the actual tuft of fibres to be shown at trial.
A blood sample was taken from Willard R. on 1 May, 2003. DI Leary testimony.
A blood sample was taken from Harold S. on 1 May, 2003. DI Leary testimony.
Harold S. denial that he was one of the intruders. Harold S. testimony.
Harold S denial that he punched the security guard Willard R. Harold S. testimony.
Harold S. was wearing a jumper and jeans at the time of his arrest. DI Leary
testimony plus the jumper and jeans to be shown at trial.
A spray pattern of blood was found on the front and right sleeve of the jumper
belonging to Harold S. DI Leary testimony plus the jumper to be shown at trial.
The blood type of the blood on the Harold S's jumper matches the blood type of the
security guard Willard R. DI Leary testimony plus tangible records of the blood match
to be shown at trial.
The tuft of red fibres found on the metal grille on the Blackbread premises was red
acrylic. DI Leary testimony plus the tuft of fibres to be shown at trial.
Harold S's jumper is made of red acrylic fibres. DI Leary testimony plus the jumper to
be shown at trial.
The tuft of red fibres found on the metal grille on the Blackbread premises is visually
indistinguishable from the fibres on Harold S's jumper. DI Leary testimony plus the
tuft of fibres and Harold S's jumper to be shown at trial.
The tuft of red fibres found on the metal grille on the Blackbread premises is
indistinguishable from the fibres on Harold S's jumper as shown in a
microspectroflourimetry analysis. DI Leary testimony plus tangible results of this
analysis to be shown at trial.
The tuft of red fibres found on the metal grille on the Blackbread premises is
indistinguishable from the fibres on Harold S's jumper as shown in a thin layer
chromatography analysis. DI Leary testimony plus tangible results of this analysis to
be shown at trial.
The jumper belonging to Harold S. is well worn and has several holes in it. DI Leary
testimony plus the jumper to be shown at trial.
None of the 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. DI Leary testimony.
By my count, taking into consideration the corroborating evidence to be shown at trial
such as photos, jumpers, jeans, test results, and so on, there are 39 items of information that I
must chart in Wigmorean terms. This is another reason why I have said that Phil's example is not
a toy problem.
3.4 Marshaling Trifles Under the Given Penultimate Probanda
Here is a vital stage in Wigmorean analysis that is so commonly overlooked. Even
Anderson and Twining do not dwell on its importance. Given a collection of evidence such as we
have in Phil's example, the first task we must perform is to marshal or organize the trifles we have
under the penultimate probanda on which we believe the trifles will bear. In fact, such marshaling
may be necessary in order to see what ultimate probandum and penultimate probanda we will
generate in the first place. In fact, this is how I generated the ultimate and penultimate probanda
in this example. So, here is how I have sorted out the trifles in this example under each one of the
four penultimate probanda I have generated under the penultimate probandum U, as given
above.
6
Trifles bearing On:
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 N. W. 8.
1). An unknown number of persons entered the premises of the Blackbread Brewery in
the early morning hours of 1 May, 2003. DI Leary testimony.
2) The persons entered the premises of the Blackbread Brewery by means of a hole that
they cut in a metal grille. DI Leary testimony plus a photo showing the hole.
3) After entering the Blackbread premises the intruders were confronted by a security
guard named Willard R. Willard R testimony.
4) Upon seeing the intruders, the security guard set off an alarm. Willard R. testimony.
7) The intruders left the Blackbread premises just as a police patrol car arrived. Willard R.
testimony.
10) There were four intruders. Willard R. testimony.
11) The security guard could not describe the intruders. Willard R. testimony.
12) The light was poor at the time of the intrusion. Willard R. testimony.
13) The security guard was confused because of the blow he had received. Willard R.
testimony.
14) The police in the patrol car that had arrived at the Blackbread premises saw the
intruders from a considerable distance away. DI Leary testimony.
Trifles Bearing On:
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.
8) The intruders' getaway car left immediately at the first sound of the alarm leaving the
intruders stranded. Willard R. testimony.
9) The intruders dispersed from the Blackbread premises on foot. Willard R. testimony.
15) In a search of the area surrounding the Blackbread premises, police apprehended
Harold S. trying to "hot wire" a car in an ally about 1/4 mile from the Blackbread
premises. DI Leary testimony plus a photo of Harold S. taken just after he was
apprehended.
16) During a police investigation a short time after the intrusion, a tuft of red fibres was
found on a jagged end of one of the cut edges of the metal grille on the Blackbread
premises. DI Leary testimony plus the actual tuft of fibres to be shown at trial
19) Harold S. denial that he was one of the intruders. Harold S. testimony.
21) Harold S. was wearing a jumper and jeans at the time of his arrest. DI Leary
testimony plus the jumper and jeans to be shown at trial.
24) The tuft of red fibres found on the metal grille on the Blackbread premises was red
acrylic. DI Leary testimony plus the tuft of fibres to be shown at trial.
25) Harold S's jumper is made of red acrylic fibres. DI Leary testimony plus the jumper to
be shown at trial.
26) The tuft of red fibres found on the metal grille on the Blackbread premises is visually
indistinguishable from the fibres on Harold S's jumper. DI Leary testimony plus the tuft of
fibres and Harold S's jumper to be shown at trial.
27) The tuft of red fibres found on the metal grille on the Blackbread premises is
indistinguishable from the fibres on Harold S's jumper as shown in a
microspectroflourimetry analysis. DI Leary testimony plus tangible results of this analysis
to be shown at trial.
28) The tuft of red fibres found on the metal grille on the Blackbread premises is
indistinguishable from the fibres on Harold S's jumper as shown in a thin layer
chromatography analysis. DI Leary testimony plus tangible results of this analysis to be
shown at trial.
7
29) The jumper belonging to Harold S. is well worn and has several holes in it. DI Leary
testimony plus the jumper to be shown at trial.
30) None of the 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. DI Leary testimony.
Trifles Bearing On:
P3: A security guard at the Blackbread Breweries, Willard R., was assaulted and
injured during the break-in at the Blackbread Breweries on 1 May, 2003.
5) After he set off the alarm, the security guard Willard R. was punched in the face by one
of the intruders. Willard R. testimony.
6)The punch Willard R. received from one of the intruders caused Willard R's nose to
bleed. Willard R. testimony plus a photo of his injury taken shortly after the incident.
Trifles Bearing On:
P4: It was Harold S. who intentionally assaulted and injured Willard R.
during the break-in at Blackbread Breweries on 1 May, 2003.
17) A blood sample was taken from Willard R. on 1 May, 2003. DI Leary testimony.
18) A blood sample was taken from Harold S. on 1 May, 2003. DI Leary testimony.
20) Harold S denial that he punched the security guard Willard R. Harold S. testimony.
22) A spray pattern of blood was found on the front and right sleeve of the jumper
belonging to Harold S. DI Leary testimony plus the jumper to be shown at trial.
23) The blood type of the blood on the Harold S's jumper matches the blood type of the
security guard Willard R. DI Leary testimony plus tangible records of the blood match to
be shown at trial.
Now, the fun begins as I attempt to construct Wigmorean arguments that will establish
the relevance of each of these trifles on one or more of the four penultimate probanda in this
example.
4.0 WIGMORE CHARTS AND KEY LISTS
Wigmore's method for making sense out of a mass of evidence has two essential
elements: analysis and synthesis. The analytic element consists of identifying all evidence items
[directly relevant and ancillary evidence], an ultimate probandum, a collection of penultimate
probanda, interim probanda [sources of doubt lurking between evidence and penultimate
probanda], and generalizations that license links in chains of reasoning set up by directly relevant
evidence. The listing and identification of these propositions is called a Key List. The synthetic
element consists of constructing a chart [an inference network we would say] that shows what the
person constructing the network believes are the inferential linkages among elements on a key
List. So, all the nodes on the network being constructed are identified by a number that appears
on the Key List.
At the close of my analysis I will have some comments to make about how process
models compares with the following Wigmorean analysis. For now, however, I will just mention
my standpoint again. As the attorney who may eventually bring this case to trial, it is my basic job
to establish the relevance, credibility and probative force credentials of the evidence we have so
far on the four penultimate probanda I have identified for this example. I do this by constructing
arguments from the evidence to these penultimate probanda, since what I am given is an
emerging collection of evidence whose probative or credentials I am trying to establish. This is
why the arrows [inferential linkages] go from the evidence to the penultimate probanda.. In the
following analysis I have constructed a chart for each one of the four penultimate probanda in this
8
example. There are some problems here that I will address later on; they involve the capturing of
possible conditional nonindependencies.
4.1 Chart and Key List for Penultimate Probandum P1.
NOTE: on this chart, and on those that follow the numbering of nodes on a chart
corresponds with the numbering of these items on its associated key list.
P1
23
0
28
16
24
0
22
0
1
15
3
5
2
21
25
9
7
11
12
13
14
27
17
19
26
4
6
8
18
20
10
CHART 1
KEY LIST FOR CHART 1
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 N. W. 8.
1) An unknown number of persons entered the premises of the Blackbread Brewery in the early
morning hours of 1 May, 2003.
2) DI Leary testimony to 1).
3) There were four intruders who entered the Blackbread Brewery premises.
4) Security Guard Willard R. testimony to 3)
5) Upon seeing the intruders, I set off an alarm.
6) Willard R. testimony to 5)
7) The intruders were confronted by the security guard.
8) Willard R testimony to 7).
9) I could not describe the intruders.
10) Willard R. testimony to 9)
11) The light was poor at the time of the intrusion.
12) Willard R. testimony to 11). [This is ancillary evidence]
13) I was confused because of the blow I received from one of the intruders.
14) Willard R. testimony to 13). [This is ancillary evidence].
15) The security guard Willard R. believed the four men to be intruders on the Blackbread
Brewery premises.
9
16) The four men who entered the Blackbread Brewery premises on 1 May, 2003 had no
authorization to do so.
17) The four intruders left the Blackbread premises just as a police patrol car arrived.
18) Willard R. testimony to 17.
19) The police in the patrol car saw the four men from a considerable distance away.
20) DI Leary testimony to 19)
21) The four men were trying to avoid apprehension by the police.
22) The four men knew that they were not authorized to enter the Blackbread Brewery premises.
23) The entry of the four men on the premises of Blackbread Brewery was illegal.
24) The four men entered the Blackbread Brewery premises by means of a hole they cut in a
metal grille on these premises.
25) DI Leary testimony to 24).
26) A photograph of the hole in the metal grille on the Blackbread Brewery premises to be shown
at trial.
27) The photograph shown at trial is the same one taken by the police shortly after the break-in at
the Blackbread Brewery on 1 May, 2003. [This is a necessary authentication probandum].
28) The entry of the four men onto the Blackbread Brewery premises on 1 May, 2003 was forced.
--------------------------------------------------------------------------------------------------------------------------------In Phil's example, we have enough evidence to infer the two major lines of argument
concerning the break-in charge; they are given by my 23 and 28 in the above key list. On my
understanding, as prosecutor I have to show that the entry of the four men onto the premises of
the Blackbread Brewery was illegal and that it was forced.
4.2 Chart and Key List for Penultimate Probandum P2.
P2
39
73
74
38
33
72
54
47
52
29
31
48
46
55
44
37
67
59
58
51
34
71
63
66
62
40
30
32
69
49
43
35
45
36
53
50
64
56
57
60
61
65
68
41
42
70
CHART 2
_____________________________________________________________________________
10
KEY LIST FOR CHART 2
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.
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.
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.
11
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 identfied 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.
___________________________________________________________________________
4.3 Chart and Key List for Penultimate Probandum P3.
We don't have much evidence for P3, so it will be quite simple.
P3
82
75
81
77
76
80
78
79
CHART 3
_____________________________________________________________________________
KEY LIST FOR CHART 3
P3: A security guard at the Blackbread Breweries, Willard R., was assaulted and
injured during the break-in at the Blackbread Breweries on 1 May, 2003.
75) After Willard R. set off the alarm he was punched in the face by one of the intruders.
76) Willard R testimony to 75).
77) The punch Willard R received from one of the intruders caused Willard R's nose to bleed.
78) Willard R. testimony to 77).
79) A photo of Willard R's injury to be shown at trial.
80) The photo shown at trial is the same one taken by the police a short time after the break-in on
1 May, 2003.
12
81) The punch Willard R. received was strong enough to cause him injury.
82) The punch Willard R. received was intended to disable him.
_____________________________________________________________________________
4.4 Chart and Key List for Penultimate Probandum P4.
P4
97
96
-
83
85
95
-
87
90
-
84
86
91
-
88
89
94
92
93
-
CHART 4
_____________________________________________________________________________
KEY LIST FOR CHART 4
P4: It was Harold S. who intentionally assaulted and injured Willard R. during the break-in
at Blackbread Breweries on 1 May, 2003.
83) A blood sample was taken from Willard R. on 1 May,2003.
84) DI Leary testimony to 83).
85) A blood sample was taken from Harold S. on 1 May, 2003.
86) DI Leary testimony to 85).
87) A spray pattern of blood was found on the front and right sleeve of the jumper belonging to
Harold R.
88) DI Leary testimony to 87).
89) The jumper showing the blood stains to be shown at trial.
90) The jumper shown at trial is the same one taken from Harold S. after his apprehension on 1
May, 2003.
91) The blood type of the blood on Harold S's jumper matches the blood type of the security
guard Willard R.
92) DI Leary testimony to 91).
93) A tangible record of the blood match analysis to be shown at trial.
94) The analysis shown at trial is the same one reported by the forensic scientist who performed
the analysis.
95) The blood on Harold S's jumper was not already there before the break-in on 1 May, 2003
96) The blood on Harold S's jumper came from Willard R.s nose on 1 May, 2003.
97) Harold S's testimonial denial of P4, that he was the one who punched the security guard
Willard R. on 1 May, 2003.
_____________________________________________________________________________
13
5.0 PROBABILISTIC EXPERT SYSTEMS AND WIGMORE CHARTS: A COMPARISON
Here is a collection of thoughts I have had as I worked through Phil's example using a
Wigmorean interpretation. The different graphical approaches Phil and I have used in the
example both make sense and are each useful for various purposes. By inspection, you can see
that my Wigmore charts are DAGs as is Phil's process model. So, both of our structural models
satisfy the basic requirement of eventual probabilistic analyses using Bayes's nets.
5.1 Decomposition Level
Asked to say what the major difference is between Phil's and my analysis, I will say that it
is the level of task decomposition imposed by my adopting the standpoint of a prosecuting
attorney. Phil's model has 12 nodes 5, but my Wigmore charts have 102. My four Wigmore charts
have one ultimate probandum, four penultimate probanda, 57 interim probanda, and 40 evidence
nodes. What accounts for this difference? First, to use William Twining's description, evidential
analyses in law cases have the advantage of having materiality criteria. What this means is that,
once I decided upon an ultimate probandum, substantive law tells me exactly what specific
elements I must prove [the penultimate probanda] in order to prove the ultimate probandum at
some specified forensic standard of proof. In my present example this standard is beyond
reasonable doubt since it involves a criminal case. The field of law is the only one known to me
that provides such materiality criteria. The ultimate and penultimate probanda [matters to be
proved] are the major sources of doubt in any case. But there are many others as well. These
other sources of doubt are identified by interim probanda that are believed to lurk between our
evidence and the penultimate probanda. Chains of interim probanda form the arguments from
evidence to penultimate probanda. In my analysis I identified 57 interim probanda or interim
sources of doubt. To use current inference network terminology, each probandum or source of
doubt is a probabilistic variable. So, I have a total of 63 probabilistic variables in my analysis.
Another decomposition matter concerns the parsing of evidence, which I mentioned
above in Section 3.2 [page 4] As a prosecuting attorney, I do have to pay great attention to the
individual "trifles" or details that items of information reveal. Some of these trifles may seem
relevant [directly or indirectly] but others not relevant. To use a currently popular metaphor,
attorneys [as well as intelligence analysts] have lots of "dots" to try to connect. We first have to
identify what dots are available and then decide what dots we will connect. But then we must also
decide which connections to make and then decide what these connections mean. In inference
network terms, I must try to establish what I believe to be the probabilistic linkage patterns among
the nodes on my networks. Evidential trifles are one form of "dot"; other dots come in the form of
the three classes of probanda I mentioned above: ultimate, penultimate, and interim. So, one way
of looking at Wigmore's analytic and synthetic methods is that they form a strategy for
"connecting the dots". Our intelligence services are just now beginning to appreciate how useful
these methods can be. As we found out to our great distress on 9/11/01, trifles [dots] and their
connections do matter, in some cases very much.
There are some troubles here for any form of inference network analysis. First, there are
no uniquely correct networks possible in any kind of analysis known to me. Someone can always
come along and identify a node you left out. Or, this person might quibble about how you have
defined the probandum or probabilistic variable in any part of your network structure. The worst
case, of course, is when a critic finds a non sequitur or disconnect in your probabilistic argument.
In law, there are often choices to be made about which probandum a given item of evidence
seems most relevant. And, there may even be arguments about what penultimate probanda are
required in an analysis. On page 4 above, I identified what seemed to be the major charge that
could be leveled at the suspect in Phil's example case. What I then did was simply to parse this
ultimate probandum into the four penultimate probanda that form the basis for my four charts. I
5
See Figure 1 in reference cited in footnote 2 above.
14
did this without any knowledge of what English law might require as penultimate probanda in
such a case. William Twining can advise me where I went wrong, if I did.
Finally, Wigmorean methods seem to be the epitome of compulsive behavior. How much
time should anyone spend in trying to identify sources of doubt that may be interposed between
our evidence and what we are trying to prove from it? Wigmore would perhaps argue that such
compulsive behavior is justified in trials at law when individual lives, freedom and fortunes are at
stake. In the intelligence world, thousands of lives and very much fortune may be at stake. In
such instances we should do our best to identify as many sources of doubt as we can. In my work
with Jay Kadane on the Sacco and Vanzetti evidence I came to believe that two innocent men
were convicted and executed because hundreds of sources of reasonable doubt, stemming from
admitted evidence, were never exposed during their trial or during their appeals process 6.
5.2 Structural Details
The most obvious feature of the four charts I have constructed for Phil's example is that
they are hierarchical or tree-like structures, the single root [or trunk] being the ultimate
probandum. Phil's PES structure is not hierarchical, in part because there are several roots. In
examining finished Wigmore charts of any kind it seems advisable to start at the top of the chart
and work downward. Thus, in my charts, the four penultimate probanda represent what are my
four major lines of argument on ultimate probandum U. Now take penultimate probandum P1 as
an example and ask the question: What are Dave's major lines of argument on P1? There are
two, as given by my 23 and 28 in Chart 1 [page 9]. Then, take 23 and ask: What were Dave's
major lines of argument on 23? Chart 1 shows that my 16 and 22 are my major lines of argument
on node 23. This is how we usually grade the Wigmorean assignments we give to our law
students. If there are inadequacies or non sequiturs at the top of a chart, everything else below it
falls off the tree.
But now comes the issue: How does one begin to construct a Wigmore chart: from the
top, from the bottom, or somewhere in between? When we are given a mass of evidence and
asked to make sense out of it, the obvious answer is: start at the bottom, with the evidence. This
is where the virtue of careful evidence marshaling comes in, as I noted in section 3.4 [pages 6 8]. The reasoning Wigmore advocated, and which I have employed in my analysis, is from
evidence to penultimate probanda. This is why the arrows or arcs on my Wigmorean networks go
upward and not downward. In order to do a Bayesian analysis of one of my charts I could simply
reverse the direction of the arcs in order to meet the requirements of the Bayes's nets software
system I have [ERGO]. This is what Jay Kadane and I did in some of our analyses of the Sacco
and Vanzetti evidence.
One class of ingredients I did leave off my charts contains the generalizations that license
or warrant each specific link in my chains of reasoning. Chronic sloth on my part is the only
reason. Here are some examples of generalizations I could have inserted. What happens in
many analyses is that generalizations are left implicit or in the background, unless a part of the
argument may be especially controversial.
1) Link 2 -> 1 on Chart 1. Here DI Leary testifies that an unknown number of persons
entered the premises of the Blackbread Brewery in the early morning hours of 1 May, 2003. As
prosecutor, I ask the jury to believe that this event did occur. In other words, how do I justify the
link between nodes 2 and 1? I assert the following generalization: "When a police officer,
testifying under oath, says that an event has occurred, then this event has probably, often,
usually, commonly occurred". [I would have to choose one of these hedges here].
6
Kadane, J., Schum, D. A Rrobabilistic Analysis of the Sacco and Vanzetti EVidence. John WIley
& Sons, NY, 1996.
15
2) Link 77 -> 81 on Chart 3. Node 77 says that the punch Willard R received from one of
the intruders caused Willard's nose to bleed. From this I ask the jury to infer 81, that the punch
Willard received was strong enough to cause him injury. As a generalization licensing this
inference, I might say: "If a blow to the body causes blood to flow, then almost certainly, very
often, very probably this blow resulted in an injury".
It is customary in Wigmorean charting to identify nodes in ways that are consistent with
the arguments the constructor is trying to establish. In my analysis, having adopted the standpoint
of prosecutor, I will identify nodes by propositions I wish to prove. For example, consider node 16
in Chart 1. Here is how I identify this node on the key list for Chart 1: "The four men who entered
the Blackbread Brewery premises on 1 May, 2003 had no authorization to do so". It is understood
completely that there is another proposition associated with node 16 and it reads: "The four men
who entered the Blackbread Brewery premises on 1 May 2003 did have authorization to do so".
Recall my earlier comment about how in law we try always to describe binary event/proposition
classes at each node. But only one state of each binary class is usually listed. What is given at
each node would not be an appropriate probabilistic variable unless it contained two or more
events/propositions. To keep key lists as simple as possible, only those events/propositions
consistent with the constructor's argument are actually listed.
Finally, I did notice one or two instances in which someone could argue that Phil and I
have drawn different conclusions from the evidence. As an example, I will first cite the evidence
of the spray pattern of blood on Harold S's jumper [my 88 and 89 on chart 4]. Phil argues that this
pattern of blood sheds light on whether or not it might be a self stain 7. I agree here completely
except that I state this conclusion a bit differently and base it on a different item of evidence. In
my 91 -> 95 link I have the following inferential step: Because the blood type on Harold S's
jumper matches the blood type of the security guard Willard R., we can infer that this blood on
Harold S's jumper was not already there before the break-in on 1 May, 2003. Phil could easily
argue that my 95 more appropriately belongs above my 87 rather than above my 91. I would not
disagree, in part because my 83, 85, 95 and 91 would then still converge to allow the inference of
96, that the blood on Harold S's jumper came from Willard R's nose on 1 May, 2003.
5.3. Evidential Subtleties and Conditional Dependence.
Wigmore was no probabilist; this would be asking too much of a person having so many
other skills relating to evidence, inference and discovery. Thus, there are none of his example
charts that reveal linkages that today we would say involve conditional dependence. But this does
not mean at all that Wigmore charting precludes the capturing of what in conventional probability
are called conditional dependence relations. This concept, in my view, is the major mechanism in
ordinary probability theory [based Kolmogorov's axioms and his definition of a conditional
probability] that allows us to capture for study and analysis a remarkable array of evidential and
inferential subtleties. I devoted the better part of a book to the capturing of these subtleties in
Bayesian terms8. It would be a major difficulty if we could not incorporate conditional
dependencies in Wigmorean evidence charting. But, of course we can do so; following is an
example involving the capture of an important evidential subtlety called synergism. Two or more
items of evidence, taken jointly, might mean something quite different than they would do if taken
separately or independently. My example comes from Chart 3.
In this chart it seems that my 75 and 81 are separate or independent lines of reasoning
on my 82. But, someone can easily argue: "If event 75 did occur, this would make event 81 more
strongly favor event 82". Substantively, if we knew that, after Willard R. set off the alarm he was
punched in the face by one of the intruders [75], this would add to the inferential force, on the
intruders' intent to disable Willard [82], of knowing that the punch that Willard received was strong
7
See ref. #2 at page 227.
Schum, D. Evidential Foundations of Probabilistic Reasoning. Wiley, NY, 1994; Northwestern
University press, 2001 [paperback].
8
16
enough to injure him [81]. To capture this synergistic subtlety, all I have to do is to insert a link
from node 75 to node 81.
Earlier I mentioned that there is a difficulty associated with breaking a Wigmore chart up
into pieces or sectors. In many cases this is necessary because of the level of detail captured in
the analysis. William Twining is the record-holder in such matters; he once had a student who
turned in a Wigmore chart that was 37 feet in length. How to break a Wigmore chart into sectors
calls for some ingenuity. Every case is different and involves careful judgment. In my present
analysis I have a separate chart for each of the four penultimate probanda in the case at hand. I
came close to the necessity of breaking my Chart 2 into sub-sectors in order to get it on one
page. It could happen, of course, that an interim probandum in one chart could be linked to one in
a different chart in order to capture some inferential subtlety. Jay Kadane and I faced this problem
since we ended up with 28 sectors in our overall Wigmore chart for the Sacco and Vanzetti
evidence. The conditional dependencies we did capture were confined within individual chart
sectors. Thus, we may have missed some that involved interim probanda in different chart
sectors.
5.4 PES and Wigmore: Common Virtues
I'll close by listing some common virtues of Phil's PES methods and Wigmore charting. I
believe some of these virtues to be frequently overlooked. The charting that is involved in PES
and in Wigmore's methods is, I believe, a device for enhancing the process of discovery. In
Wigmore evidence charting, each source of doubt identified in argument construction opens up a
new line of inquiry and potential evidence. For example, consider interim probandum 38 in Chart
2. The prosecutor would be alerted by this interim probandum to verify the identity of the actual
owner of the car Harold S. was trying to "hot wire". Harold might claim that the car was his and
that he had simply lost his keys. The prosecutor would be quite embarrassed if, at trial, the
defense produced an authentic document showing that Harold S. did own the car he was trying to
"hot wire". I believe the same discovery virtues accompany Phil's PES methods. In trying to
capture some complex process, a stage of this process might be generated that opens up an
entirely new line of investigation that no one had previously identified.
Here's another discovery-related matter about which both a PES and a Wigmore analysis
can offer assistance; it concerns the sufficiency of evidence or, in Baconian terms, the
completeness of coverage of available evidence on matters to be proved at trial. As a prosecutor
in the case of Harold S., I would need to come up with additional lines of argument, backed by
evidence, on some of the penultimate probanda in this case. My present argument on P3 seems
rather skimpy. Perhaps someone looking at Phil's model, or Phil himself, might observe the
necessity for adding more probabilistic variables and considering new lines of evidence.
Graphical methods can certainly assist in determining the sufficiency of the ingredients some
model involves.
Both PES and Wigmorean methods have appeal for persons having particular
standpoints. As Phil's example illustrates, the forensic scientist has different objectives than does
a prosecuting attorney. For example, in the forensic sciences efforts are made to understand
various physical processes that can cause the emergence of various forms of trace evidence
such as blood samples, glass fragments, shell casings and so on. Having models of these
processes is of great assistance in interpreting the significance of the way in which these forms of
trace evidence emerged. Such information is of course vital to attorneys who will subsequently
make use of this information at trial. But attorneys, such as the prosecutor in my analysis, operate
under proof-related constraints that do not encumber the forensic scientist. There are evidential
admissibility constraints as we all recognize. In addition, our Anglo-American trial system is
adversarial and so, as a prosecuting attorney, I had to try to anticipate all the sources of doubt
that the defense might raise concerning the evidence I intended to offer at trial. This is essentially
what Wigmore had in the back of his mind as he devised his analytic and synthetic methods.
17
I believe that both the PES and Wigmorean methods assist attorneys in the narratives
they will use in opening and closing arguments. Both methods allow attorneys [and others, such
as intelligence analysts, using these models] to tell coherent and persuasive stories that are more
appropriately anchored on the evidence available. But there are other stories to be told that both
methods allow. In either a PES or in a Wigmorean analysis one can tell a variety of different
probabilistic stories by inserting different combinations of numerical ingredients into these
inferential models. Bayesian inference engines applied in either approach simple allow us to
observe how each one of these stories ends. Jay Kadane and I told a wide variety of different
stories about the probative force of items and collections of the Sacco and Vanzetti evidence.
Some stories we told on behalf of the prosecution; others we told on behalf of the defense. Given
more time, I could easily have told such probabilistic stores regarding the present case of Harold
S. I would simply have applied my ERGO system to any of my four Wigmore charts.
Finally, both the PES and Wigmorean analyses are devices for allowing us to make
sense out of situations having great complexity. There are certain attributes of any complex
process and both PES and Wigmorean methods provide ways for incorporating most of these
complexity attributes in our attempts to make sense out of masses of evidence.
18