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 this:
+The network would look something like in figere~\ref{bnnetworkhouses}
+
+\begin{tabular}{|l|l|}
+ \hline
+ Joe &\\
+ \hline
+ T & $\nicefrac{5}{7}$\\
+ F & $\nicefrac{2}{7}$\\
+ \hline
+\end{tabular}
+\begin{tabular}{|l|l|}
+ \hline
+ William &\\
+ \hline
+ T & $\nicefrac{5}{7}$\\
+ F & $\nicefrac{2}{7}$\\
+ \hline
+\end{tabular}
+\begin{tabular}{|l|l|}
+ \hline
+ Jack & \\
+ \hline
+ T & $\nicefrac{5}{7}$\\
+ F & $\nicefrac{2}{7}$\\
+ \hline
+\end{tabular}
+\begin{tabular}{|l|l|}
+ \hline
+ Averall & \\
+ \hline
+ T & $\nicefrac{5}{7}$\\
+ F & $\nicefrac{2}{7}$\\
+ \hline
+\end{tabular}
+
+\begin{tabular}{|llll|ll|}
+ \hline
+ & & & & Burglary &\\
+ Joe & William & Jack & Averall & T & F\\
+ \hline
+ F& F& F& F & $0$ & $1$\\
+ F& F& F& T & $0$ & $1$\\
+ F& F& T& F & $0$ & $1$\\
+ F& F& T& T & $0$ & $1$\\
+ F& T& F& F & $0$ & $1$\\
+ F& T& F& T & $0$ & $1$\\
+ F& T& T& F & $0$ & $1$\\
+ F& T& T& T & $0$ & $1$\\
+ T& F& F& F & $0$ & $1$\\
+ T& F& F& T & $0$ & $1$\\
+ T& F& T& F & $1$ & $0$\\
+ T& F& T& T & $0$ & $1$\\
+ T& T& F& F & $1$ & $0$\\
+ T& T& F& T & $0$ & $1$\\
+ T& T& T& F & $1$ & $0$\\
+ T& T& T& T & $1$ & $0$\\
+ \hline
+\end{tabular}
+\begin{tabular}{|lll|}
+ \hline
+ & Holmes &\\
+ Burglary & T & F\\
+ \hline
+ T & $0.000153$ & $0.999847$\\
+ F & $0$ & $1$\\
+ \hline
+\end{tabular}
+
\begin{figure}[H]
\caption{Bayesian network of burglars and houses}
- \label{bnetwork21}
+ \label{bnnetworkhouses}
\centering
\includegraphics[scale=0.5]{d2.eps}
\end{figure}