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P(cancer | positive x-ray & positive CT scan) = 0.96
Here, we are going to show you that our new framework of reasoning will help us to get the
result easier. The following is the analysis and steps of finding the answer:
First, we decide what is the question: after read the problem statement, we know the
question is: P(cancer | positive x-ray & positive CT scan) = ?
Second, we calculate the degree for the prior probability (having cancer in a population) and
the degrees for the two tests (x-ray and CT scan):
degree(prior)
= 10 log
10
(0.002) = - 27
(get from 2:998)
degree(x-ray)
= 10 log
10
(14.17) = 11.5
(get from 0.85/0.06)
degree(CT scan) = 10 log
10
(850)
= 29.3
(get from 0.85/0.001)
Third, we get the overall degree by adding all above degree values:
degree(answer)
= 13.8
Fourth, we extract the answer in terms of probability by using Formula 7:
strength(answer) = 10
degree(answer) / 10
= 10
13.8 / 10
= 23.99
Convert to probability, it equals P = 23.99 / (23.99 + 1) = 0.96
Thus the final answer is:
P(cancer | positive x-ray & positive CT scan) = 0.96
(same value as the one got in Example 2)
As you can see, our evidence based reasoning is easier than the original Bayes' theorem in
dealing with many evidences. One thing to point out is that our evidence based reasoning
can be used in many areas. For example, in bioinformatics, data mining, category
classification, etc., just to name a few.
7. Knowledge management in bio-information system architecture
We described the fundamentals of computer reasoning and proposed an
EvidenceBasedReasoning algorithm. In this section, we will introduce a framework of
knowledge management in the context of bio-information system architectures. Based on
this framework, we will introduce a prototype implementation of the Bio-information
knowledge management system.
7.1 Knowledge management framework
In a typical knowledge management system, there are many components. Figure 5 shows an
information system architecture upon which we base our reasoning framework and
knowledge management methods.
