C1. Likelihood, prior and posterior

Topic: Bayesian foundations · more questions on this topic
‹ Q16 C5 ›

What are a likelihood, a prior and a posterior? Which variable is the likelihood a function of after observing the data?

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Definitions/notation. For observed data x and parameter \theta, the likelihood L(\theta;x)=p(x\mid\theta) is a function of \theta, the prior p(\theta) describes parameter uncertainty before these data, and the posterior p(\theta\mid x)\propto L(\theta;x)p(\theta) describes it after observing them. The likelihood need not integrate to one over \theta.