Weight of Evidence, Explanation
and Test Selection
Two of the more interesting features of rule-based expert systems are:
If we would like to use graphical models like expert systems, we
should explore what we mean by test selection and explantaion.
- their ability to "explain" their actions, and
- their ability to "select" the next test.
Unfortunately, there are a lot of different ways we can explain the
behavior of a model. I have chosen the following definition which
observations (instantiated variables) are most influential in regards
to our current hypothesis. This leads naturally to the definition of
the weight of evidence.
Suppose we have a target hypothesis H whose state we are trying
to establish. For example, we may be trying to establish whether or
not a patient has coronary artery disease. In this particular case,
we may wish to know the influence that a finding E has on our
information about H. I.J. Good (Many
references) suggests the weight of
as a metric for the explanatory power of an observation. Note that
the weight of evidence is a signed quantity, observations which
increate the probability of H have positive weight of evidence,
those which decrease the probability of H have negative weight
We can also use weight of evidence to help guide the selection of the
next test (variable to observe). Suppose that a test T has n
possible outcomes, . The
expected weight of evidence is the expected value (average) of the the
weight of evidence under the assumption that the hypothesis is true,
Expected weight of evidence is a quasi-utility: it plays the role that
a formal utility might play in a more formal decision analysis. In
particular, expected weight of evidence is a stand-in for value of
Obviously, we want to select tests with high weight of evidence (or
value of information if we have a full decision model).
Unfortunately, it is seldom that straightforward in real world
problems because we need to account for (1) the cost of testing and
(2) the fact that tests come in bunches. Madigan and
Almond go into more detail.
Graphical-Belief implements four kinds of
Madigan, Mosurski and Almond  describe these
explanation tools in more detail. One intriguing technique they
described which is not discussed here is the evidence chain, coloring
the edges of a graph to represent strength of evidence flow. Although
we experimented with those ideas in
Graphical-Belief, ultimately they never proved as
useful as the simple node coloring schemes.
explanation using Probability Node Coloring.
the main example page.
Back to overview of Graphical-Belief.
View a list
of Graphical-Belief in publications and downloadable technical
The Graphical-Belief user
interface is implemented in Garnet.
information about obtaining Graphical-Belief (and why
it is not generally available).
the home page for Russell Almond , author
here to get to the home page for Insightful (the company that StatSci
has eventually evolved into).
The ideas presented in this section are further developed in the following papers:
- Madigan, D., K. Mosurski and R.G. Almond 
- ``Explanation in Belief Networks.'' Journal of
Computational and Graphical Statistics, 6, 160-181.
- Madigan, D. and R.G. Almond 
- ``Test Selection Strategies for Belief Networks'' StatSci
Research Report 20. Presented at the 5th International
Workshop on AI and Statistics
Describes the use of weight of evidence to select tests.
I.J. Good develops the mathematics and philosophy of weight of
evidence in many references including:
- Good, I.J. 
- Probability and the Weighing of Evidence. Charles
- Good, I.J. 
- ``Rational Decisions.'' JRSS Series B (14),
- Good, I.J. 
- ``The probabilistic explication of information, evidence,
surprise, causality, explanation and utility.'' In Proceedings of
a Symposium on the Foundations of Statistical Inference, Holt,
Rinehart and Winston. 108--141.
- Good, I.J. and W. Card 
- ``The diagnostic process with special reference to errors.''
Method of Inferenential Medicine. (10), 176--188.
- Good, I.J. }
- Good Thinking University of Minnesota Press.
- Good, I.J. 
- ``Weight of Evidence: A brief survey.'' In Bernardo,
J. DeGroot, M. Lindley, D. and Smith, A. (eds.) Bayesian
Statistics 2, North Holland, 249--269.
The following paper first introduces the idea of the evidence balance
sheet in the context of a simple ("Idiot Bayes") model:
- Spiegelhalter, D and R Knill-Jones 
- ``Statistical and knowledge-based approaches to clinical decision
support systems, with an application in gastroenterology.''
Journal of the Royal Statistical Society, (Series A), (
John Tukey suggest in the discussion that the evidence balance sheet
should be made "graphical". The evidence
balance sheet shown is our implementation of that idea.
Russell Almond, <lastname> (at) acm.org
Last modified: Mon Aug 19 15:58:39 1996