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mhjensen
2017-12-13 12:19:05 +01:00
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commit ee0c838c83
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doc/pub/Bayesian/html/._Bayesian-bs000.html
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<title>Data Analysis and Machine Learning: Elements of Bayesian theory</title>
<!-- Bootstrap style: bootstrap -->
<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<!-- not necessary
<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
-->
<style type="text/css">
@@ -39,7 +39,8 @@ Automatically generated HTML file from DocOnce source
</head>
<!-- tocinfo
{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
{'highest level': 2,
'sections': [('What is Bayesian Statistics', 2, None, '___sec0')]}
end of tocinfo -->
<body>
@@ -61,7 +62,7 @@ end of tocinfo -->
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._Bayesian-bs001.html#___sec0" style="font-size: 80%;">Introduction</a></li>
<!-- navigation toc: --> <li><a href="._Bayesian-bs001.html#___sec0" style="font-size: 80%;">What is Bayesian Statistics</a></li>
</ul>
</li>
@@ -96,7 +97,7 @@ end of tocinfo -->
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Sep 20, 2017</h4></center> <!-- date -->
<center><h4>Dec 13, 2017</h4></center> <!-- date -->
<br>
<p>
@@ -117,8 +118,8 @@ end of tocinfo -->
</div> <!-- end container -->
<!-- include javascript, jQuery *first* -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<!-- Bootstrap footer
<footer>
doc/pub/Bayesian/html/._Bayesian-bs001.html
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<title>Data Analysis and Machine Learning: Elements of Bayesian theory</title>
<!-- Bootstrap style: bootstrap -->
<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<!-- not necessary
<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
-->
<style type="text/css">
@@ -39,7 +39,8 @@ Automatically generated HTML file from DocOnce source
</head>
<!-- tocinfo
{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
{'highest level': 2,
'sections': [('What is Bayesian Statistics', 2, None, '___sec0')]}
end of tocinfo -->
<body>
@@ -61,7 +62,7 @@ end of tocinfo -->
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Introduction</a></li>
<!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">What is Bayesian Statistics</a></li>
</ul>
</li>
@@ -77,12 +78,19 @@ end of tocinfo -->
<a name="part0001"></a>
<!-- !split -->
<h2 id="___sec0" class="anchor">Introduction </h2>
<h2 id="___sec0" class="anchor">What is Bayesian Statistics </h2>
<div class="panel panel-default">
<div class="panel-body">
<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
Say something more general here. Reminder about probabilities from the statistics section
<p>
<ol>
<li> Product rule</li>
<li> Binomial distribution</li>
<li> Gaussian PDF</li>
<li> other PDFs</li>
<li> Bayesian regression analysis</li>
</ol>
</div>
</div>
@@ -98,8 +106,8 @@ end of tocinfo -->
</div> <!-- end container -->
<!-- include javascript, jQuery *first* -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<!-- Bootstrap footer
<footer>
doc/pub/Bayesian/html/Bayesian-bs.html
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<title>Data Analysis and Machine Learning: Elements of Bayesian theory</title>
<!-- Bootstrap style: bootstrap -->
<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
<!-- not necessary
<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
-->
<style type="text/css">
@@ -39,7 +39,8 @@ Automatically generated HTML file from DocOnce source
</head>
<!-- tocinfo
{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
{'highest level': 2,
'sections': [('What is Bayesian Statistics', 2, None, '___sec0')]}
end of tocinfo -->
<body>
@@ -61,7 +62,7 @@ end of tocinfo -->
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._Bayesian-bs001.html#___sec0" style="font-size: 80%;">Introduction</a></li>
<!-- navigation toc: --> <li><a href="._Bayesian-bs001.html#___sec0" style="font-size: 80%;">What is Bayesian Statistics</a></li>
</ul>
</li>
@@ -96,7 +97,7 @@ end of tocinfo -->
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Sep 20, 2017</h4></center> <!-- date -->
<center><h4>Dec 13, 2017</h4></center> <!-- date -->
<br>
<p>
@@ -117,8 +118,8 @@ end of tocinfo -->
</div> <!-- end container -->
<!-- include javascript, jQuery *first* -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
<!-- Bootstrap footer
<footer>
doc/pub/Bayesian/html/Bayesian-reveal.html
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\
<!DOCTYPE html>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
@@ -131,7 +132,7 @@ td.padding {
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Sep 20, 2017</h4></center> <!-- date -->
<center><h4>Dec 13, 2017</h4></center> <!-- date -->
<br>
<p>
@@ -142,10 +143,19 @@ td.padding {
<section>
<h2 id="___sec0">Introduction </h2>
<h2 id="___sec0">What is Bayesian Statistics </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
Say something more general here. Reminder about probabilities from the statistics section
<ol>
<p><li> Product rule</li>
<p><li> Binomial distribution</li>
<p><li> Gaussian PDF</li>
<p><li> other PDFs</li>
<p><li> Bayesian regression analysis</li>
</ol>
</div>
</section>
doc/pub/Bayesian/html/Bayesian-solarized.html
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<script src="https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_styles/style_solarized_box/js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<link href="http://thomasf.github.io/solarized-css/solarized-light.min.css" rel="stylesheet">
<link href="https://thomasf.github.io/solarized-css/solarized-light.min.css" rel="stylesheet">
<style type="text/css">
h1 {color: #b58900;} /* yellow */
/* h1 {color: #cb4b16;} orange */
@@ -59,7 +59,8 @@ div { text-align: justify; text-justify: inter-word; }
</head>
<!-- tocinfo
{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
{'highest level': 2,
'sections': [('What is Bayesian Statistics', 2, None, '___sec0')]}
end of tocinfo -->
<body>
@@ -85,17 +86,24 @@ end of tocinfo -->
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Sep 20, 2017</h4></center> <!-- date -->
<center><h4>Dec 13, 2017</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec0">Introduction </h2>
<h2 id="___sec0">What is Bayesian Statistics </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
Say something more general here. Reminder about probabilities from the statistics section
<ol>
<li> Product rule</li>
<li> Binomial distribution</li>
<li> Gaussian PDF</li>
<li> other PDFs</li>
<li> Bayesian regression analysis</li>
</ol>
</div>
doc/pub/Bayesian/html/Bayesian.html
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@@ -64,7 +64,8 @@ div { text-align: justify; text-justify: inter-word; }
</head>
<!-- tocinfo
{'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0')]}
{'highest level': 2,
'sections': [('What is Bayesian Statistics', 2, None, '___sec0')]}
end of tocinfo -->
<body>
@@ -90,17 +91,24 @@ end of tocinfo -->
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Sep 20, 2017</h4></center> <!-- date -->
<center><h4>Dec 13, 2017</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec0">Introduction </h2>
<h2 id="___sec0">What is Bayesian Statistics </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
Say something more general here. Reminder about probabilities from the statistics section
<ol>
<li> Product rule</li>
<li> Binomial distribution</li>
<li> Gaussian PDF</li>
<li> other PDFs</li>
<li> Bayesian regression analysis</li>
</ol>
</div>
doc/pub/Bayesian/ipynb/Bayesian.ipynb
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@@ -7,20 +7,31 @@
"<!-- dom:TITLE: Data Analysis and Machine Learning: Elements of Bayesian theory -->\n",
"# Data Analysis and Machine Learning: Elements of Bayesian theory\n",
"<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
"<!-- Author: --> **Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"<!-- Author: --> \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
"Date: **Sep 20, 2017**\n",
"Date: **Dec 13, 2017**\n",
"\n",
"Copyright 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
"\n",
"\n",
"\n",
"## Introduction"
"## What is Bayesian Statistics\n",
"Say something more general here. Reminder about probabilities from the statistics section\n",
"1. Product rule\n",
"\n",
"2. Binomial distribution\n",
"\n",
"3. Gaussian PDF\n",
"\n",
"4. other PDFs\n",
"\n",
"5. Bayesian regression analysis"
]
}
],
"metadata": {},
"nbformat": 4,
"nbformat_minor": 1
"nbformat_minor": 2
}
doc/pub/Bayesian/ipynb/ipynb-Bayesian-src.tar.gz
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doc/pub/How2ReadData/ipynb/How2ReadData.ipynb
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doc/pub/How2ReadData/ipynb/Untitled.ipynb
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doc/src/Bayesian/Bayesian.do.txt
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!split
===== What is Bayesian Statistics =====
!bblock
Say something general here. Reminder about probabilities from the statistics section
Say something more general here. Reminder about probabilities from the statistics section
o Product rule
o Binomial distribution
o Gaussian PDF
o other PDFs
!eblock
!split
===== Bayesian regression analysis =====
!bblock
!bt
\[
mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})\right).} \rho(\mathbf{y}|\mathbf{X},\boldsymbol\beta,\sigma^{2}) \propto (\sigma^{2})^{-n/2} \exp\left(-\frac{1}{2{\sigma}^{2}}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)^{\rm T}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)\right).
\]
!et
The ordinary least squares solution is to estimate the coefficient vector using the Moore-Penrose pseudoinverse:
!bt
\[
{\hat {\boldsymbol {\beta }}=(\mathbf {X} ^{\rm {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\rm {T}}\mathbf {y} } \hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1}\mathbf{X}^{\rm T}\mathbf{y}
\]
!et
where
!bt
\[
{\displaystyle \mathbf {X} } \mathbf {X}
\]
!et
is the ${n\times k n \times k$ design matrix, each row of which is a predictor vector $\mathbf {x} _{i}^{\rm {T}} \mathbf{x}_{i}^{\rm T}$ and $\mathbf {y} \mathbf {y}$ is the column $n$-vector $[y_{1}\;\cdots \;y_{n}]^{\rm {T}} [y_1 \; \cdots \; y_n]^{\rm T}$.
o Bayesian regression analysis
!eblock