update

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

diff --git a/report/ass2-1.tex b/report/ass2-1.tex
index aa53fe7..d487425 100644 (file)
--- a/report/ass2-1.tex
+++ b/report/ass2-1.tex
@@ -1,22 +1,38 @@
-
 \chapter{Probabilistic representation and reasoning (and burglars)}
 \section{Bayesian network and the conditional probability tables}
 \begin{figure}[H]
        \caption{Bayesian network, visual representation}
        \centering
-       %\includegraphics[scale=0.5]{d1.eps}
+       \includegraphics[scale=0.5]{d1.eps}
 \end{figure}
-\strut\\
+
+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).
+$$\frac{1}{365 + 0.25 - 0.01 - 0.0025}=\frac{1}{365.2425}$$
+
+This gives the following probability distributions\\
 \begin{tabular}{|l|ll|}
        \hline
-       & \multicolumn{2}{c|}{Radio}\\
-       Earthquake & T & F\\
+       & \multicolumn{2}{c|}{Earthquake}\\
        \hline
-       T & $0.9998$ & $0.0002$\\
-       F & $0.0002$ & $0.9998$\\
+       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|}{$I_1$}\\
@@ -26,7 +42,6 @@
        F & $0$ & $1$\\
        \hline
 \end{tabular}
-%
 \begin{tabular}{|l|ll|}
        \hline
        & \multicolumn{2}{c|}{$I_2$}\\
@@ -36,7 +51,6 @@
        F & $0$ & $1$\\
        \hline
 \end{tabular}
-%
 \begin{tabular}{|ll|ll|}
        \hline
        && \multicolumn{2}{c|}{Alarm}\\
@@ -48,7 +62,7 @@
        F & F & $0$ & $1$\\
        \hline
 \end{tabular}
-%
+
 \begin{tabular}{|l|ll|}
        \hline
        & \multicolumn{2}{c|}{Watson}\\
@@ -58,7 +72,6 @@
        F & $0.4$ & $0.6$\\
        \hline
 \end{tabular}
-%
 \begin{tabular}{|l|ll|}
        \hline
        & \multicolumn{2}{c|}{Gibbons}\\
@@ -67,4 +80,13 @@
        T & $0.99$ & $0.01$\\
        F & $0.04$ & $0.96$\\
        \hline
-\end{tabular}
\ No newline at end of file
+\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}