mhjensen
209 lines
10 KiB
HTML
209 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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<!-- 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="._Bayesian-bs004.html#___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="part0008"></a>
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<blockquote>
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As this scenario appears quite far-fetched, we might be inclined to think of [Fig. 1.2] in terms of the distribution of the measurements of the mass in many repetitions of the experiment. Although we are at liberty to think about a problem in any way that facilitates its solution, or our understanding of it, having to seek a frequency interpretation for every data analysis problem seems rather perverse.
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For example, what do we mean by the ‘measurement of the mass’ when the data consist of orbital periods? Besides, why should we have to think about many repetitions of an experiment that never happened? What we really want to do is to make the best inference of the mass given the (few) data that we actually have; this is precisely the Bayes and Laplace view of probability.
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</blockquote>
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<li><a href="._Bayesian-bs007.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><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 class="active"><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="._Bayesian-bs014.html">15</a></li>
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<li><a href="._Bayesian-bs015.html">16</a></li>
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<li><a href="._Bayesian-bs016.html">17</a></li>
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<li><a href="._Bayesian-bs017.html">18</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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