hallo'

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

diff --git a/report/ass2-1.tex b/report/ass2-1.tex
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--- a/report/ass2-1.tex
+++ b/report/ass2-1.tex
@@ -1,70 +1,110 @@
-
 \chapter{Probabilistic representation and reasoning (and burglars)}
-\section{Bayesian network and the conditional probability tables}
+\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}
+       \includegraphics[scale=0.5]{d1.eps}
 \end{figure}
-\strut\\
-\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}
-%
-\begin{tabular}{|l|ll|}
-       \hline
-       & \multicolumn{2}{c|}{$I_1$}\\
-       Earthquake & T & F\\
-       \hline
-       T & $0.2$ & $0.08$\\
-       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}\\
-       i1 & i2 & 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}
\ No newline at end of file
+
+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}