An empirical Bayes method estimates prior hyperparameters from the marginal distribution of the observed data and then uses the resulting fitted prior in Bayesian inference.
A maximum marginal likelihood estimator chooses a hyperparameter by maximizing the data density obtained after integrating the model parameter against its prior distribution.
A hyperparameter controls a family of prior distributions or statistical models and is fixed, estimated, or assigned a further prior at a higher level of a hierarchical model.
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