Mathematics

Bayesian Inference

Bayesian inference is how rational agents update beliefs in light of new evidence. It is arguably the mathematics of learning itself. In clinical medicine, every diagnostic test result shifts our prior probability of disease toward a posterior probability via likelihood ratios. The brain itself appears to be a Bayesian inference engine — the predictive processing framework proposes that perception is not passive reception but active prediction, with sensory data serving as evidence that updates an internal generative model of the world.