hallo'

[ker2014-2.git] / report / ass2-1.tex

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 \chapter{Probabilistic representation and reasoning (and burglars)}
+\section{Formal description}
+In our representation of the model we chose to introduce a \textit{Noisy OR} to
+represent the causal independence of \textit{Burglar} and \textit{Earthquake}
+on \textit{Alarm}. The visual representation of the network is visible in
+Figure~\ref{bnetwork21}
+
+\begin{figure}[H]
+       \caption{Bayesian network, visual representation}
+       \label{bnetwork21}
+       \centering
+       \includegraphics[scale=0.5]{d1.eps}
+\end{figure}
+
+As for the probabilities for \textit{Burglar} and \textit{Earthquake} we chose
+to calculate them using days the unit. Calculation for the probability of a
+\textit{Burglar} event happening at some day is then this(assuming a gregorian
+calendar and leap days).
+$$\frac{1}{365 + 0.25 - 0.01 - 0.0025}=\frac{1}{365.2425}$$
+
+This gives the following probability distributions visible in
+Table~\ref{probdist}
+
+\begin{table}[H]
+       \label{probdist}
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{Earthquake}\\
+               \hline
+               T & $0.0027$ & $0.9972$ \\
+               F & $0.9973$ & $0.0027$\\
+               \hline
+       \end{tabular}
+       %
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{Burglar}\\
+               \hline
+               T & $0.0027$ & $0.9973$ \\
+               F & $0.9973$ & $0.0027$\\
+               \hline
+       \end{tabular}
+       
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{$I_1$}\\
+               Earthquake & T & F\\
+               \hline
+               T & $0.2$ & $0.8$\\
+               F & $0$ & $1$\\
+               \hline
+       \end{tabular}
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{$I_2$}\\
+               Burglar & T & F\\
+               \hline
+               T & $0.95$ & $0.05$\\
+               F & $0$ & $1$\\
+               \hline
+       \end{tabular}
+       \begin{tabular}{|ll|ll|}
+               \hline
+               && \multicolumn{2}{c|}{Alarm}\\
+               $I_1$ & $I_2$ & T & F\\
+               \hline
+               T & T & $1$ & $0$\\
+               T & F & $1$ & $0$\\
+               F & T & $1$ & $0$\\
+               F & F & $0$ & $1$\\
+               \hline
+       \end{tabular}
+       
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{Watson}\\
+               Alarm & T & F\\
+               \hline
+               T & $0.8$ & $0.2$\\
+               F & $0.4$ & $0.6$\\
+               \hline
+       \end{tabular}
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{Gibbons}\\
+               Alarm & T & F\\
+               \hline
+               T & $0.99$ & $0.01$\\
+               F & $0.04$ & $0.96$\\
+               \hline
+       \end{tabular}
+       \begin{tabular}{|l|ll|}
+               \hline
+               & \multicolumn{2}{c|}{Radio}\\
+               Earthquake & T & F\\
+               \hline
+               T & $0.9998$ & $0.0002$\\
+               F & $0.0002$ & $0.9998$\\
+               \hline
+       \end{tabular}
+\end{table}
+
+\section{Implementation}
+This distribution results in the \textit{AILog} code in Listing~\ref{alarm.ail}
+
+\begin{listing}
+       \label{alarm.ail}
+       \caption{Alarm.ail}
+       \inputminted[linenos,fontsize=\footnotesize]{prolog}{./src/alarm.ail}
+\end{listing}