esis is then calculated with its assigned conditional probability (either based on prior knowledge or assigned randomly if no prior knowledge is present) of each of the possible outcomes. This step simply assigns the probability of observing each outcome if that particular hypothesis is true. The unique part of Bayes' theorem, and what was new in the 18th century, is one then makes note of which outcome actually occurred and can then compute revised prior probabilities for the hypothesis, (See equation 2), based on the actual outcome. CHAPTER IV MEDICAL USE OF BAYES THEOREMSuppose you undergo a medical test for a relatively rare cancer. Your doctor tells you the cancer has an incidence of 1% in the general population. In other words, the chance of you having the cancer is one in one hundred, i.e. a probability of 0.01. The test is known to be 89% reliable. That is, the test will not fail to find cancer when present, but will give a positive result in 11% percent of the cases where no cancer is present, this is known as a false positive.When you are tested, the test yields a positive result. The question is, given the result of the test, what is the probability that you have cancer. It is easy to assume that if the test is nearly 75% accurate, and you test positive, then the likelihood you have the cancer is about 75%. That assumption is way off. The actual likelihood you have cancer is merely 3.9% (i.e., the probability is 0.039). Three point nine percent is still something to worry about with cancer but hardly as daunting as 75%. The problem is, that the 75% reliability factor for the test, has to be balanced against the fact that only 1% of the entire population has the cancer. Using Bayes' method ensures you make proper use of the information available.As I have discussed, Bayes' method allows you to calculate the probability of a certain event C (in the above event, having the cancer), based on evidence (e.g. the ...
