report/ass2-1.tex

   1 \chapter{Probabilistic representation and reasoning (and burglars)}
   2 \section{Formal description}
   3 In our representation of the model we chose to introduce a \textit{Noisy OR} to
   4 represent the causal independence of \textit{Burglar} and \textit{Earthquake}
   5 on \textit{Alarm}. The visual representation of the network is visible in
   6 Figure~\ref{bnetwork21}
   7
   8 \begin{figure}[H]
   9         \caption{Bayesian network, visual representation}
  10         \label{bnetwork21}
  11         \centering
  12         \includegraphics[scale=0.5]{d1.eps}
  13 \end{figure}
  14
  15 As for the probabilities for \textit{Burglar} and \textit{Earthquake} we chose
  16 to calculate them using days the unit. Calculation for the probability of a
  17 \textit{Burglar} event happening at some day is then this(assuming a gregorian
  18 calendar and leap days).
  19 $$\frac{1}{365 + 0.25 - 0.01 - 0.0025}=\frac{1}{365.2425}$$
  20
  21 This gives the following probability distributions visible in
  22 Table~\ref{probdist}
  23
  24 \begin{table}[H]
  25         \label{probdist}
  26         \begin{tabular}{|l|ll|}
  27                 \hline
  28                 & \multicolumn{2}{c|}{Earthquake}\\
  29                 \hline
  30                 T & $0.0027$ & $0.9972$ \\
  31                 F & $0.9973$ & $0.0027$\\
  32                 \hline
  33         \end{tabular}
  34         %
  35         \begin{tabular}{|l|ll|}
  36                 \hline
  37                 & \multicolumn{2}{c|}{Burglar}\\
  38                 \hline
  39                 T & $0.0027$ & $0.9973$ \\
  40                 F & $0.9973$ & $0.0027$\\
  41                 \hline
  42         \end{tabular}
  43
  44         \begin{tabular}{|l|ll|}
  45                 \hline
  46                 & \multicolumn{2}{c|}{$I_1$}\\
  47                 Earthquake & T & F\\
  48                 \hline
  49                 T & $0.2$ & $0.8$\\
  50                 F & $0$ & $1$\\
  51                 \hline
  52         \end{tabular}
  53         \begin{tabular}{|l|ll|}
  54                 \hline
  55                 & \multicolumn{2}{c|}{$I_2$}\\
  56                 Burglar & T & F\\
  57                 \hline
  58                 T & $0.95$ & $0.05$\\
  59                 F & $0$ & $1$\\
  60                 \hline
  61         \end{tabular}
  62         \begin{tabular}{|ll|ll|}
  63                 \hline
  64                 && \multicolumn{2}{c|}{Alarm}\\
  65                 $I_1$ & $I_2$ & T & F\\
  66                 \hline
  67                 T & T & $1$ & $0$\\
  68                 T & F & $1$ & $0$\\
  69                 F & T & $1$ & $0$\\
  70                 F & F & $0$ & $1$\\
  71                 \hline
  72         \end{tabular}
  73
  74         \begin{tabular}{|l|ll|}
  75                 \hline
  76                 & \multicolumn{2}{c|}{Watson}\\
  77                 Alarm & T & F\\
  78                 \hline
  79                 T & $0.8$ & $0.2$\\
  80                 F & $0.4$ & $0.6$\\
  81                 \hline
  82         \end{tabular}
  83         \begin{tabular}{|l|ll|}
  84                 \hline
  85                 & \multicolumn{2}{c|}{Gibbons}\\
  86                 Alarm & T & F\\
  87                 \hline
  88                 T & $0.99$ & $0.01$\\
  89                 F & $0.04$ & $0.96$\\
  90                 \hline
  91         \end{tabular}
  92         \begin{tabular}{|l|ll|}
  93                 \hline
  94                 & \multicolumn{2}{c|}{Radio}\\
  95                 Earthquake & T & F\\
  96                 \hline
  97                 T & $0.9998$ & $0.0002$\\
  98                 F & $0.0002$ & $0.9998$\\
  99                 \hline
 100         \end{tabular}
 101 \end{table}
 102
 103 \section{Implementation}
 104 This distribution results in the \textit{AILog} code in Listing~\ref{alarm.ail}
 105
 106 \begin{listing}
 107         \label{alarm.ail}
 108         \caption{Alarm.ail}
 109         \inputminted[linenos,fontsize=\footnotesize]{prolog}{./src/alarm.ail}
 110 \end{listing}