Definition
A Bayesian update is the act of revising how strongly you believe something after seeing new evidence. You start with a prior — your estimate before the evidence — and adjust it to a posterior estimate based on how much the new information actually distinguishes between the possibilities.
The key insight is that evidence does not overwrite a belief; it nudges it. How far it nudges depends on two things: how confident you were before, and how surprising the evidence would be if the belief were false versus true.
Why it matters
How it works
In practice, ask three questions: How likely did I think this was before? How expected is what I just observed if the belief is true? How expected is it if the belief is false? Strong evidence is evidence that is far more likely under one hypothesis than the other; it moves the estimate a lot. Ambiguous evidence moves it little.
The discipline is to hold beliefs as probabilities and shift them in proportion to the strength of what you learn — never more, never less.