X-Git-Url: https://git.martlubbers.net/?a=blobdiff_plain;f=report%2Fass2-1.tex;h=7f2b15f69612d60b83d9595938d4ffb903602011;hb=5c232e0aecd71d51f950bab6006b66a75713f0de;hp=aa53fe7be5bd1d274e26e7f2ec6ad1391800d9c8;hpb=d497f146fda6032301cba9ecdcbdca4344e9d35d;p=ker2014-2.git

diff --git a/report/ass2-1.tex b/report/ass2-1.tex
index aa53fe7..7f2b15f 100644
--- 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}\\
-	$I_1$ & $I_2$ & 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}
\ 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}