hallo'
authorMart Lubbers <mart@martlubbers.net>
Tue, 6 Jan 2015 10:00:36 +0000 (11:00 +0100)
committerMart Lubbers <mart@martlubbers.net>
Tue, 6 Jan 2015 10:00:36 +0000 (11:00 +0100)
report/.gitignore
report/Makefile
report/ass2-1.tex
report/report.out [deleted file]

index 9ee4f69..2101d8a 100644 (file)
@@ -5,4 +5,5 @@
 *.pyg
 *.toc
 *.eps
+*.out
 *.synctex.gz
index 5d2fcdf..ab49026 100644 (file)
@@ -9,7 +9,7 @@ graphs:
        dot -Teps d1.dot > d1.eps 
 
 clean:
-       rm -vf *.eps report.{aux,dvi,log,pyg,toc,eps,synctex.gz}
+       rm -vf *.eps report.{aux,out,dvi,log,pyg,toc,eps,synctex.gz}
 
 clobber: clean
        rm -vf report.pdf
index deaa133..7f2b15f 100644 (file)
 \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}
 \end{figure}
 
-We introduced a \textit{Noisy OR} to represent the causal independence of
-\textit{Burglar} and \textit{Earthquake} on Alarm. Probabilities for the causes
-of the alarm are calculated using days, in practice this means that the
-smallest discrete time interval is one day. The calculation for the probability
-of a burglar is then calculated with the following formula(taking leap years
-into account and assuming a standard gregorian calendar).
+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\\
-\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}
+This gives the following probability distributions visible in
+Table~\ref{probdist}
 
-\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}
+\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}
 
-\paragraph{Implementation}\strut\\
+\section{Implementation}
 This distribution results in the \textit{AILog} code in Listing~\ref{alarm.ail}
 
 \begin{listing}
diff --git a/report/report.out b/report/report.out
deleted file mode 100644 (file)
index 00945ba..0000000
+++ /dev/null
@@ -1,3 +0,0 @@
-\BOOKMARK [0][-]{chapter.1}{Probabilistic representation and reasoning \(and burglars\)}{}% 1
-\BOOKMARK [1][-]{section.1.1}{Bayesian network and the conditional probability tables}{chapter.1}% 2
-\BOOKMARK [0][-]{chapter.2}{Visual representations and reasoning}{}% 3