Definition
Plain language
Updating what you believe as new evidence comes in, by combining your starting guess with how well each option fits the data.
As stated in the literature
Computing a posterior distribution from a prior and a likelihood via Bayes' rule; invoked in the RL-as-inference equivalence, where the optimal KL-regularized policy is exactly a reward-tilted posterior over the base model's outputs.
Also called: Bayes' rule, Bayesian update
Why it matters: It gives a principled way to combine prior knowledge with fresh evidence, which is the backbone of reasoning under uncertainty.
For example, if you think a coin is probably fair but then see it land heads ten times in a row, Bayesian inference tells you how to shift your belief toward it being biased.
Heard on the show
“Through Bayes' rule, and the intuition is the only thing you need.”Episode 170 — When a One-Liner Beats Your Agent's Clever Verification Logic