Information Technology Reference
In-Depth Information
Evidence Theory and Evidence Properties
The Main Interest:
Suppose that A represents an event of interest; E represents the a piece
of envidence. The main interest of the evidence theory is to calculate the probability:
P(A|E)
(Formula 4)
Definition of Evidence:
we define evidence (or a test) E as a piece of information that has the
ability to change the value of probability defined in Formula 4. The underlining reason for
this ability is the causality relationship existed between the event A and the evidence E.
Assumption about Event A:
in the absence of any evidence, we will assume that the
probability of event A occurring is the same as the probability of its not occurring. That is,
P(A) = 50%.
Properties of Evidence:
evidence has following three properties:
Property 1:
if evidence E increases the probability of event A, then the evidence E is
positive evidence relative to event A.
Property 2:
if evidence E decreases the probability of event A, then the evidence E is
negative evidence relative to event A.
Property 3:
the quality of evidence E is measured in terms of evidence strength (which will
be defined in the next section).
6.2 The quality of evidence (evidence strength)
As mentioned before, one important function of a piece of evidence is its influence on a
rational mind. Thus, the quality measurement of a piece of evidence should also be based on
its ability to influence. For example, if evidence A convinced us an event (or goal
achievability) will happen with 80 percent certainty while evidence B convinced us the same
event will happen with 90 percent certainty, then we would say evidence B is better. We can
quantify the quality of evidence by introducing the concept of evidence strength. With this
measurement criterion in mind, try to answer the following question:
Question 1:
With regard to the two tests mentioned in Example 2: the x-ray test, and the CT
scan test, which one is better in swaying us to believe that the person in question has lung
cancer?
Here is the repeat of some statistics for the two evidences (a medical test can be regarded as
evidence from Bayes' theorem's point of view):
X-ray test: 85% of the people with lung cancer will show positive; 6% of the people
without lung cancer will also show positive.
CT scan test: 85% of the people with lung cancer will show positive; 0.1% of the people
without lung cancer will also show positive.
Before answering the above question, let's define some terms. In the following,
“Posi|Cause” means that the existence of “Cause” causes the evidence “Posi” to appear;
“Posi|~Cause” means that the absence of “Cause” causes the evidence “Posi” to appear.
Now, we will define the strength of evidence as follows:
