AP Statistics Curriculum 2007 Bayesian Hierarchical - Revision history

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Jenny at 21:16, 28 June 2010

2010-06-28T21:16:36Z

IvoDinov at 23:34, 22 October 2009

2009-10-22T23:34:46Z

JayZzz: New page: 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 $\theta...$

2009-06-02T06:04:22Z

New page: 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...

New page

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 we 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==

==Hierarchical Normal Model==

==Stein Estimator==

==Bayesian analysis for unknown overall mean==

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ==[[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; when the <math>\eta</math> is unknown we have a second tier in which we suppose we 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.
+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==

← Older revision		Revision as of 23:34, 22 October 2009
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		+	==[[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; when the <math>\eta</math> is unknown we have a second tier in which we suppose we 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.		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 we 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.

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	==Bayesian analysis for unknown overall mean==		==Bayesian analysis for unknown overall mean==
		+
		+
		+	==See also==
		+	* [[EBook#Chapter_III:_Probability \|Probability Chapter]]
		+
		+	==References==
		+
		+	<hr>
		+	* SOCR Home page: http://www.socr.ucla.edu
		+
		+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Bayesian_Hierarchical}}

AP Statistics Curriculum 2007 Bayesian Hierarchical - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

Jenny at 21:16, 28 June 2010

IvoDinov at 23:34, 22 October 2009

JayZzz: New page: 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...

JayZzz: New page: 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 $\theta...$