Adding motivation to BNN

doc/pub/Bayesian/html/Bayesian.html

@@ -66,7 +66,7 @@ div { text-align: justify; text-justify: inter-word; }
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('What is Bayesian Statistics', 2, None, '___sec0'),
+ 'sections': [('Why Bayesian Statistics?', 2, None, '___sec0'),
               ('Inference', 2, None, '___sec1'),
               ('Statistical Inference', 2, None, '___sec2'),
               ('Some history', 2, None, '___sec3'),
@@ -149,24 +149,34 @@ MathJax.Hub.Config({
 <center>[3] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Jun 7, 2019</h4></center> <!-- date -->
+<center><h4>Jun 8, 2019</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec0">What is Bayesian Statistics  </h2>
+<h2 id="___sec0">Why Bayesian Statistics?  </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
-Morten's original plan: 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>
+<p>
+We have already made ourselves familiar with elements of a statistical
+data analysis via quantities like the bias-variance tradeoff as well
+as some central distribution functions such as the Normal
+distribution, the binomial distribution and other probability
+distribution functions.
+
+<p>
+In essentially all the Machine Learning
+algorithms we have studied, our focus has been on a so-called
+<b>frequentist approach</b>, where knowledge of an underlying likelihood
+function has not been emphasized. Our data, whether we had a classification or a regression problem, have been our central points of departure.
+
+<p>
+Here we wish to merge this approach with the derivation of a likelihood function which can be used to make prediction on how our system under study evolves. 
+We will venture into the realm of what is called Bayesian Neural Networks. To get an overarching view on what this entails, the following figure conveys the essential differences between a standard Neural network that we have met earlier and a Bayesian Neural Network. In order to get there, we need to present some of the basic elements of Bayesian statistics, starting with the product rule and Bayes' theorem.
+
+
 </div>