Information Technology Reference
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The assumption of this method is that each piece of evidence is independent. Because of the
strength of Bayes' theorem, this assumption works even for evidences that are not
independent. Studies show that systems based on Bayes' theorem with the same assumption
such as Hidden Naïve Bayes (Jin & et al., 2007) are robust because of the model constructing
can accommodate minor factors easily. The reason for this robustness stems from the fact
that the model itself has already captured the main causality. Any other accuracy
consideration does not improve too much. In a sense, it only adds the complexity.
Our reasoning method can be represented as the following algorithm:
EvidenceBasedReasoning Algorithm: Inputs: raw data, input question of probability of
an event of interest; Output: posterior probability information (answer to the input
question)
Step 1: constructing models (or knowledge) from raw data.
Step 2: calculate the quality of evidence related to the input question in terms of evidence
degree with the help of Formulas 6 and 7.
Step 3: calculate the overall evidence degree.
Step 4: interpret the information by converting the overall evidence degree back to the
probability (using Formulas 6 and 7 again).
We have the following comments about the degree of evidence:
1.
The critical point for the degree of evidence is 0. 0 means the evidence is neutral; the
probability of positive conditional is equal to the probability of negative conditional. It
does not add anything in shifting our view to the world.
2.
If the evidence's degree is greater than 0, then it will shift our view toward believing
event A is true; if the evidence's degree is less than 0, then it will shift our view toward
believing event A is not true;
3.
Degree is measured in terms of order of degree. If evidence A's degree is 10 and
evidence B's degree is 20, then evidence B is ten order of magnitude (100 times)
stronger than evidence A in persuasion power.
Now, let's use an example to illustrate how our EvidenceBasedReasoning works.
Example 4:
Solve the problem in Example 2 again using the EvidenceBasedReasoning
algorithm. We repeat the main points and assumptions in the following:
1.
About 0.2% of the population living in US with age above 20 has lung cancer.
2.
When doing an annual check, assume that 85% of the people with lung cancer will
show positive for the chest x-ray test. About 6% of the people without lung cancer will
also show positive for the chest x-ray test.
3.
The second test called CT scan is done independently. It returns positive for 85% of the
people with lung cancer; its false rate is 0.1%.
4.
If a person went through the annual check and had positives on both the chest x-ray
and the CT scan, what is the probability that he/she has the lung cancer?
Answer:
We will solve this problem using the EvidenceBasedReasoning algorithm. Using
Bayes' theorem, we already solved the problem and knew the correct answer for that
question is
