Bayes' rule: Guide

Abstract

Bayes’ rule is a fundamental principle in probability theory that governs how to update beliefs in the face of new evidence. This guide presents Bayes’ rule in various forms, starting with an intuitive explanation using frequency diagrams and waterfall diagrams. It then introduces the odds form of Bayes’ rule, which expresses the relationship between prior odds, likelihood ratio, and posterior odds. The guide further explores the theoretical implications of Bayes’ rule, emphasizing its role in scientific reasoning and decision-making. It discusses the concept of “least surprise” and how Bayes’ rule helps us to revise our beliefs in a systematic way. Additionally, it touches upon the log-odds form and the proportional form of Bayes’ rule, providing a comprehensive understanding of this essential tool for probability and statistics. – AI-generated abstract