The standard Bayesian model is defined in terms of an outcome model and the prior density of the parameters. The latter depends on parameters called hyperparameters. A hierarchical Bayes model results when one or more of the hyperparameters are assumed to be random and modelled probabilistically. We discuss canonical versions of these models for the case when both the parameters and the hyperparameters are modelled in groups or blocks, provide relevant examples, and discuss how inference by Markov chain Monte Carlo methods makes even the fitting of complex hierarchical models practical and simple. The problem of model comparisons is also addressed.
Bayes’ th Component densities Exchangeability Hierarchical Bayes models Hyperparameters Marginal likelihood Markov chain Monte Carlo methods
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