Likelihood
Likelihood is how probable the observed evidence is under a specific hypothesis, used to update beliefs.
Definition
Likelihood describes how consistent evidence is with a hypothesis. It is often phrased as the probability of observing evidence given the hypothesis, which is a form of conditional probability.
Why it matters
Likelihood is the raw ingredient for Bayes updates. Comparing likelihood under two hypotheses yields a likelihood ratio, which updates prior odds into posterior odds.
Common pitfalls
Confusing with probability of the hypothesis: Likelihood is about evidence given hypothesis, not hypothesis given evidence.
Ignoring base rates: Evidence without a base rate is incomplete.