Difference between revisions of "AP Statistics Curriculum 2007 Bayesian Hierarchical"
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==[[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 <math>\theta</math> from which observations x has density p(x|<math>\theta</math>). 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 <math>\theta_i</math> are independently and identically distributed, their common distribution might depend on a parameter <math>\eta</math> which we refer to as a hyperparameter | + | 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 <math>\theta</math> from which observations x has density p(x|<math>\theta</math>). 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 <math>\theta_i</math> are independently and identically distributed, their common distribution might depend on a parameter <math>\eta</math> which we refer to as a hyperparameter. When the <math>\eta</math> is unknown we have a second tier in which we suppose to have a hyperprior p(<math>\eta</math>) expressing our beliefs about possible values of <math>\eta</math>. In such a case we may say that we have a hierarchical model. |
==Idea of a Hierarchical Model== | ==Idea of a Hierarchical Model== | ||
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Latest revision as of 11:34, 3 March 2020
Contents
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 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
Hierarchical Normal Model
Stein Estimator
Bayesian analysis for unknown overall mean
See also
References
- SOCR Home page: http://www.socr.ucla.edu
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