7 Bayes theorem
Bayes theorem
Bayes theorem is a conditional probability that is important to many fields of risk management. Bayesian reasoning is very counterintuitive. It basically describes the actual probabilities of events based on tests for those events; i.e.: 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? The answer is 7.8%, and it is not so easy to compute. The example is explained over at the Machine Intelligence Research Institute
Understanding Bayes Theorem With Ratios