Link: Bayesian statistics Prior probability and posterior probability Conditional probabilities

What is Bayes’ theorem?

Bayes’ theorem is the basics for Bayesian statistics.

The equation:


  • = the prior probability of A occurring
  • = the conditional probability of A, given that B occurs
  • = the conditional probability of B, given that A occurs
  • = the probability of B occurring

Derive Bayes’ theorem

A simple example

Chance of a medical condition with test result

  • Prior Probability : Initial belief about having the medical condition before taking the test. E.g. 2% chance (0.02) of having a condition based on symptoms and family history.
  • Likelihood : The probability that the test is positive given that you actually have the condition. E.g. 95% (assuming the test is pretty accurate)
  • Total Evidence : The overall probability of getting a positive test result, taking into account both scenarios: having the condition (A) and not having it . So:

If we apply Bayes’ theorem:

  • : the updated probability of actually having the condition after getting a positive test result


It means we can get posterior probability based on prior probability, likelihood, and total evidence.