Bayes' theorem

Bayes' theorem is a formula for calculating the probability of an event using prior knowledge of related conditions. The theorem was discovered by an English statistician and minister named Thomas Bayes in the 18^th century. Bayes never published his work; his notes were edited and published posthumously by the mathematician Richard Price. Bayes' theorem is given by the following formula:

A and B are events; P(A) is the probability of observing event A, and P(B) is the probability of observing event B. P(A|B) is the conditional probability of observing A given that B was observed. In classification tasks, our goal is to map features of explanatory variables to a discrete response variable; we must find the most likely label, A, given the features, B.

Note

A theorem is a mathematical statement that has been proven to be true based on axioms or other theorems.

Let's work through an example. Assume that a patient exhibits a symptom of a particular disease, and that a doctor administers...