Maximum Likelihood: Maximizing the likelihood function so that, under the assumed statistical model, the observed data is most probable.
Marginal Likelihood: In Bayesian statistics, it represents the probability of generating the observed sample from a prior and is therefore often referred to as model evidence or simply evidence.
(Definition in slides: Identify probability of incomplete sample Y, with marginal probability of observed variables. If the data are missing at random then we can use the margianl likelihood similar to the way we use the standard likelihood for complete data.)
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