AP Statistics Curriculum 2007 Bayesian Hierarchical

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Sometimes we cannot be sure about the factuality of our prior knowledge. Often we make one or more assumptions about the relationships between the different unknown parameters θ from which observations x has density p(x|θ). These associations are sometimes referred to as structural. In some cases the structural prior knowledge is combined with a standard form of Bayesian prior belief about the parameters of the structure. In the case where θi are independently and identically distributed, their common distribution might depend on a parameter η which we refer to as a hyperparameter; when the η is unknown we have a second tier in which we suppose we have a hyperprior p(η) expressing our beliefs about possible values of η. In such a case we may say that we have a hierarchical model.


Idea of a Hierarchical Model

Hierarchical Normal Model

Stein Estimator

Bayesian analysis for unknown overall mean

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