Adding motivation to BNN

doc/src/Bayesian/Bayesian.do.txt

@@ -5,14 +5,23 @@ DATE: today
 
 
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-===== What is Bayesian Statistics  =====
+===== Why Bayesian Statistics?  =====
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-Morten's original plan: Reminder about probabilities from the statistics section
-o Product rule
-o Binomial distribution
-o Gaussian PDF
-o other PDFs
-o Bayesian regression analysis
+
+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.  
+
+In essentially all the Machine Learning
+algorithms we have studied, our focus has been on a so-called
+_frequentist approach_, 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. 
+
+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.
+
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