mhjensen
211 lines
10 KiB
HTML
211 lines
10 KiB
HTML
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<a class="navbar-brand" href="Bayesian-bs.html">Data Analysis and Machine Learning: Elements of Bayesian theory and Bayesian Neural Networks</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._Bayesian-bs001.html#___sec0" style="font-size: 80%;"><b>Why Bayesian Statistics?</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs002.html#___sec1" style="font-size: 80%;"><b>Inference</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs003.html#___sec2" style="font-size: 80%;"><b>Statistical Inference</b></a></li>
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<!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;"><b>Some history</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs010.html#___sec4" style="font-size: 80%;"><b>The Bayesian recipe</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs011.html#___sec5" style="font-size: 80%;"><b>Bayes' theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs013.html#___sec6" style="font-size: 80%;"><b>The friends of Bayes' theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs014.html#___sec7" style="font-size: 80%;"><b>Inference With Parametric Models</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs016.html#___sec8" style="font-size: 80%;"><b>Illustrative examples with python code</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs017.html#___sec9" style="font-size: 80%;"><b>Example: Is this a fair coin?</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs018.html#___sec10" style="font-size: 80%;"><b>A few words on different priors</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs019.html#___sec11" style="font-size: 80%;"><b>Bayesian parameter estimation (single parameter)</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec12" style="font-size: 80%;"> Example: Measured flux from a star</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec13" style="font-size: 80%;"> Simple Photon Counts: Frequentist Approach</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec14" style="font-size: 80%;"> Simple Photon Counts: Bayesian Approach</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec15" style="font-size: 80%;"> A note about priors</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec16" style="font-size: 80%;"> Simple Photon Counts: Bayesian approach in practice</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec17" style="font-size: 80%;"> Best estimates and confidence intervals</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs020.html#___sec18" style="font-size: 80%;"> Simple Photon Counts: Best estimates and confidence intervals</a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs021.html#___sec19" style="font-size: 80%;"><b>Bayesian parameter estimation (multiple parameters, covariance)</b></a></li>
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<!-- navigation toc: --> <li><a href="._Bayesian-bs022.html#___sec20" style="font-size: 80%;"><b>Bayesian model selection</b></a></li>
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<a name="part0004"></a>
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<!-- !split -->
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<h2 id="___sec3" class="anchor">Some history </h2>
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Adapted from D.S. Sivia <button type="button" class="btn btn-primary btn-xs" rel="tooltip" data-placement="top" title="Sivia, Devinderjit, and John Skilling. Data Analysis : A Bayesian Tutorial, OUP Oxford, 2006"><a href="#def_footnote_1" id="link_footnote_1" style="color: white">1</a></button>:
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<p id="def_footnote_1"><a href="#link_footnote_1"><b>1:</b></a> Sivia, Devinderjit, and John Skilling. Data Analysis : A Bayesian Tutorial, OUP Oxford, 2006</p>
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<p>
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<blockquote>
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Although the frequency definition appears to be more objective, its range of validity is also far more limited. For example, Laplace used (his) probability theory to estimate the mass of Saturn, given orbital data that were available to him from various astronomical observatories. In essence, he computed the posterior pdf for the mass M , given the data and all the relevant background information I (such as a knowledge of the laws of classical mechanics): prob(M|{data},I); this is shown schematically in the figure [Fig. 1.2].
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</blockquote>
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<p>
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<p>
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<li><a href="._Bayesian-bs003.html">«</a></li>
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<li><a href="._Bayesian-bs000.html">1</a></li>
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<li><a href="._Bayesian-bs001.html">2</a></li>
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<li><a href="._Bayesian-bs002.html">3</a></li>
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<li><a href="._Bayesian-bs003.html">4</a></li>
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<li class="active"><a href="._Bayesian-bs004.html">5</a></li>
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<li><a href="._Bayesian-bs005.html">6</a></li>
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<li><a href="._Bayesian-bs006.html">7</a></li>
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<li><a href="._Bayesian-bs007.html">8</a></li>
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<li><a href="._Bayesian-bs008.html">9</a></li>
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<li><a href="._Bayesian-bs009.html">10</a></li>
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<li><a href="._Bayesian-bs010.html">11</a></li>
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<li><a href="._Bayesian-bs011.html">12</a></li>
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<li><a href="._Bayesian-bs012.html">13</a></li>
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<li><a href="._Bayesian-bs013.html">14</a></li>
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<li><a href="">...</a></li>
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<li><a href="._Bayesian-bs022.html">23</a></li>
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<li><a href="._Bayesian-bs005.html">»</a></li>
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