Bayes's theorem is a math formula for determining conditional probability. The theorem is named after Thomas Bayes, an 18th-century mathematician from London, England. Recall that conditional probability refers to the probability of an event occurring given that another event has already occurred. For example, when you draw an ace from a deck of playing cards, this changes the probability of drawing a second ace from the same deck.
In this reading, you’ll learn more about the different parts of Bayes's theorem, and how you can use the theorem to calculate conditional probability.
Bayes's theorem provides a way to update the probability of an event based on new information about the event.
In Bayesian statistics, prior probability refers to the probability of an event before new data is collected. Posterior probability is the updated probability of an event based on new data.
Bayes’s theorem lets you calculate posterior probability by updating the prior probability based on your data.
For example, let’s say a medical condition is related to age. You can use Bayes’s theorem to more accurately determine the probability that a person has the condition based on age. The prior probability would be the probability of a person having the condition. The posterior, or updated, probability would be the probability of a person having the condition if they are in a certain age group.
Let’s examine the theorem itself.
Bayes’s theorem states that for any two events A and B, the probability of A given B equals the probability of A multiplied by the probability of B given A divided by the probability of B.
Bayes’s theorem
In the theorem, prior probability is the probability of event A. Posterior probability, or what you’re trying to calculate, is the probability of event A given event B.
Sometimes, statisticians and data professionals use the term “likelihood” to refer to the probability of event B given event A, and the term “evidence” to refer to the probability of event B.
Using these terms, you can restate Bayes’s theorem as: