# AP Statistics Curriculum 2007 Bayesian Hierarchical

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 Revision as of 23:28, 22 October 2009 (view source)IvoDinov (Talk | contribs)← Older edit Current revision as of 21:10, 28 June 2010 (view source)Jenny (Talk | contribs) Line 1: Line 1: ==[[EBook | Probability and Statistics Ebook]] - Bayesian Hierarchical Models== ==[[EBook | Probability and Statistics Ebook]] - Bayesian Hierarchical Models== - 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 $\theta$ from which observations x has density p(x|$\theta$). 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 $\theta_i$ are independently and identically distributed, their common distribution might depend on a parameter $\eta$ which we refer to as a hyperparameter; when the $\eta$ is unknown we have a second tier in which we suppose we have a hyperprior p($\eta$) expressing our beliefs about possible values of $\eta$. In such a case we may say that we have a hierarchical model. + 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 $\theta$ from which observations x has density p(x|$\theta$). 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 $\theta_i$ are independently and identically distributed, their common distribution might depend on a parameter $\eta$ which we refer to as a hyperparameter. When the $\eta$ is unknown we have a second tier in which we suppose to have a hyperprior p($\eta$) expressing our beliefs about possible values of $\eta$. In such a case we may say that we have a hierarchical model. ==Idea of a Hierarchical Model== ==Idea of a Hierarchical Model==

## Probability and Statistics Ebook - Bayesian Hierarchical Models

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 to 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.