In a Bayesian context, what term denotes the probability of the observed data given a model or hypothesis?

• A. Posterior probability
• B. Likelihood
• C. Prior probability
• D. Marginal likelihood

Answer: (B)

Likelihood is the probability of the observed data given the model parameters. It’s a function of the parameters that tells you how compatible the data are with those parameter values. In Bayes’ rule, the likelihood combines with the prior to form the posterior: p(θ|D) ∝ p(D|θ) p(θ). The prior reflects beliefs before seeing data, the posterior updates those beliefs after observing data, and the marginal likelihood (or model evidence) is the probability of the data under the model after averaging over θ, used for comparing models. For example, with a coin of unknown bias, the likelihood p(D|θ) describes how probable the observed sequence of heads and tails is for different θ values, guiding the update from prior to posterior.