Technical GlossaryMathematics, Statistics and Optimization

Bayes' Theorem

A fundamental probability theorem that allows updating the probability of a hypothesis as new observations arrive.

Bayes’ Theorem is the mathematical method for systematically updating our beliefs in light of new data. It combines prior knowledge with observed evidence to produce an updated probability. This logic is used in domains ranging from medical diagnosis and spam filtering to sensor fusion and Bayesian machine learning. The strength of the Bayesian approach lies in treating uncertainty not as a fixed number, but as an updateable structure of belief. For that reason, Bayes’ Theorem is not just a formula, but a way of thinking.