http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Bayesian_Hierarchical&feed=atom&action=historyAP Statistics Curriculum 2007 Bayesian Hierarchical - Revision history2024-03-29T12:37:33ZRevision history for this page on the wikiMediaWiki 1.15.1http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Bayesian_Hierarchical&diff=10424&oldid=prevJenny at 21:16, 28 June 20102010-06-28T21:16:36Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==[[EBook | Probability and Statistics Ebook]] - Bayesian Hierarchical Models==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==[[EBook | Probability and Statistics Ebook]] - Bayesian Hierarchical Models==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>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<del class="diffchange diffchange-inline">; when </del>the <math>\eta</math> is unknown we have a second tier in which we suppose <del class="diffchange diffchange-inline">we </del>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.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>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<ins class="diffchange diffchange-inline">. When </ins>the <math>\eta</math> is unknown we have a second tier in which we suppose <ins class="diffchange diffchange-inline">to </ins>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.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Idea of a Hierarchical Model==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Idea of a Hierarchical Model==</div></td></tr>
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</table>Jennyhttp://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Bayesian_Hierarchical&diff=9456&oldid=prevIvoDinov at 23:34, 22 October 20092009-10-22T23:34:46Z<p></p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==[[EBook | Probability and Statistics Ebook]] - Bayesian Hierarchical Models==</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>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.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Bayesian analysis for unknown overall mean==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Bayesian analysis for unknown overall mean==</div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==See also==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* [[EBook#Chapter_III:_Probability |Probability Chapter]]</ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==References==</ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">* SOCR Home page: http://www.socr.ucla.edu</ins></div></td></tr>
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</table>IvoDinovhttp://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Bayesian_Hierarchical&diff=9070&oldid=prevJayZzz: 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...2009-06-02T06:04:22Z<p>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...</p>
<p><b>New page</b></p><div>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.<br />
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==Idea of a Hierarchical Model==<br />
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==Hierarchical Normal Model==<br />
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==Stein Estimator==<br />
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==Bayesian analysis for unknown overall mean==</div>JayZzz