Knowledge Management in Bio-Information Systems - Intelligent Systems - page 52

Observation 2: strong evince is not caused by a very high probability of cause leads to the
positive test, rather it is caused by a very low probability of not-cause could have led to the
positive test.

For example, if it is raining, the grass in my front yard (there is no roof) is likely to be wet.
But seeing the grass wet does not necessarily mean that it is raining (maybe it is caused by
the sprinkler). In other words, when seeing the evidence of wet grass, we cannot reason that
it is raining with certainty. This is a case of high probability of cause-effect but week
evidence.

On the hand, if we are watching an area there is no sprinkler. Then, seeing the wet grass
would always mean that it is raining, even though we assume that there is a weak causation
link such as the rain will cause the grass wet only 60% of times. This is a case of low
probability of cause-effect but strong evidence.

Now, let's answer the Question 1. We will use the evidence strength value to help us make
the conclusion. For x-ray test, we have the following:

strength(x-ray test) = P(positive x-ray | cancer) / P(positive x-ray | ~cancer)

= 0.85 / 0.06 = 14.17

For CT scan, we have:

strength(CT scan test) = P(positive CT scan | cancer) / P(positive CT scan | ~cancer)

= 0.85 / 0.001 = 850

Since the value 850 is greater than 14.17, we conclude that CT scan test is a better evidence in
convincing us that the patient in question has lung cancer.

6.3 The relationship between the evidence strength and its influence power

The discussion above gives us some insights about evidence. In this section, we will
investigate the relationship between the evidence strength and its power to influence the
outcome of an event. Specifically, we want to see how the existence of a piece of evidence
will shift our belief (its direction and its amount (may be rough estimation)). Based on the
intuition we have about the evidence, we make the following claim.

Claim 1: the influence power of a given piece of evidence is proportional to the value of
evidence strength. For positive evidence, the larger evidence strength value, the stronger the
influence power; for negative evidence, the smaller evidence strength value, the stronger the
influence power.

We will use the following example to give some insight about our Claim 1:

Example 3: Using the data in Example 2, calculate the strength for x-ray test and the
strength for the CT scan test. Then, calculate the distance that each test moves our belief
(including the direction) in terms of percentage change. We repeat the main points and data
in the following:

1. About 0.2% of the population living in US with age above 20 has lung cancer.