# Bayes' rule

(2 hours to learn)

## Summary

Bayes' rule is a formula for combining prior beliefs with observed evidence to obtain a "posterior" distribution. It is central to Bayesian statistics, where one infers a posterior over the parameters of a statistical model given the observed data.

## Context

This concept has the prerequisites:

## Goals

• Know the statement of Bayes' Rule
• Be able to use it to combine prior information with evidence
• Derive Bayes' Rule from the definition of conditional probability
• Know terminology: prior, posterior
• Be able to reason intuitively about Bayes' Rule in terms of odds ratios

## -Free-

Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
Other notes:
• This uses the measure theoretic notion of probability, but should still be accessible without that background. Refer to Lecture 1.S for unfamiliar terms.

## -Free-

BerkeleyX: Introduction to Statistics: Probability
An online course on basic probability.
Location: Lecture 1.6, "Bayes' Rule"