Bayesian networks

diff --git a/report/ass2-1.tex b/report/ass2-1.tex
index 42931cc..6a07cda 100644 (file)
--- a/report/ass2-1.tex
+++ b/report/ass2-1.tex
@@ -240,8 +240,7 @@ We implemented the extended story using a three layered model.\\
         average this happens only 5 days a week} 
        Meaning that every burglar has the same initial working probability: 5/7 (see the first 5 lines of code).\\
 Then we implemented the constraints on the colleagues by telling ailog that a burglary can happen when at least one of our combinations is working (see line 8 to 11).\\
-\textit{Finally, if they decide to burgle, then they will burgle 3 houses a night.} The third layer consists of implementing the change that out of the 10,000 houses in which Joe, William, Jack and Averall are the only burglars, Holmes' house is burgled as one of the three (see line 14 to 19).\\
-This results in the following probability for a burglary at a Holmes' house.
+\textit{Finally, if they decide to burgle, then they will burgle 3 houses a night.} The third layer consists of implementing the change that out of the 10,000 houses in which Joe, William, Jack and Averall are the only burglars, Holmes' house is burgled as one of the three (see line 14 to 19). This results in the following probability for a burglary at a Holmes' house.
 
 $P(burglary)\cdot(
        P(\text{first house Holmes'})+
@@ -254,10 +253,21 @@ $P(burglary)\cdot(
        \approx 0.000196773$
 
 \section{Bayesian networks}
-A Bayesian network representation of the burglary problem with a multitude of
-houses and burglars is possible but would be very big and tedious because all
-the constraints about the burglars must be incorporated in the network.
-The network would look something like in figure~\ref{bnnetworkhouses}
+A Bayesian network representation of the extended story is possible, but could
+ become very large because of the great number of houses and burglars. However
+  we found a way to create a network that is very compact, see
+   figure~\ref{bnnetworkhouses} and the corresponding probability tables. The
+    network is created in the same way as our implementation of the extended
+     story. Every burglar has the same starting probabilities that are merged 
+     together in whether a burglary happens. Then the probability of a burglary
+      at Holmes' house when there will be burgled is calculated.
+
+\begin{figure}[H]
+       \caption{Bayesian network of burglars and houses}
+       \label{bnnetworkhouses}
+       \centering
+       \includegraphics[scale=0.5]{d2.eps}
+\end{figure}
 
 \begin{tabular}{|l|l|}
        \hline
@@ -325,9 +335,4 @@ The network would look something like in figure~\ref{bnnetworkhouses}
        \hline
 \end{tabular}
 
-\begin{figure}[H]
-       \caption{Bayesian network of burglars and houses}
-       \label{bnnetworkhouses}
-       \centering
-       \includegraphics[scale=0.5]{d2.eps}
-\end{figure}
+