OBJECTIVE
Identify the
probability of a hypothesis using the probability of related events.
DESCRIPTION
This probabilistic approach is often used in
logic tests, which may require a statement such as the following to be solved:
0.5% of the
population suffers a certain disease and those with this disease that take a
clinical test are diagnosed correctly in 90% of cases. You also know that you
have on average 10% of false positive tests on people who do not have the
disease. A person has been diagnosed as positive; what is the probability that
he actually has the disease?
This problem is solved
by finding the percentage of true positives (the test is positive and the
person has the disease) in the total number of positive tests, and it can be
approached by drawing the following matrix and calculating the missing percentages:
Matrix of the Bayesian Inference Method
The answer is given by
dividing 0.45% by 10.45%, giving a 4.31% possibility of that person being sick.
More formally, the problem is resolved by the following equation:
where P is the
probability, A is having the disease, and B is when the test is positive; therefore,
P(A|B) is the probability of having the disease when the test is positive and
P(B|A) is the probability of obtaining a positive test when the patient has the
disease. The template shows how the values have been calculated starting from
the proposed problem.
TEMPLATE
No comments:
Post a Comment