1 \chapter{Probabilistic representation and reasoning (and burglars)
}
2 \section{Bayesian network and the conditional probability tables
}
4 \caption{Bayesian network, visual representation
}
6 \includegraphics[scale=
0.5]{d1.eps
}
9 We introduced a
\textit{Noisy OR
} to represent the causal independence of
10 \textit{Burglar
} and
\textit{Earthquake
} on Alarm. Probabilities for the causes
11 of the alarm are calculated using days, in practice this means that the
12 smallest discrete time interval is one day. The calculation for the probability
13 of a burglar is then calculated with the following formula(taking leap years
14 into account and assuming a standard gregorian calendar).
15 $$
\frac{1}{365 +
0.25 -
0.01 -
0.0025}=
\frac{1}{365.2425}$$
17 This gives the following probability distributions\\
18 \begin{tabular
}{|l|ll|
}
20 &
\multicolumn{2}{c|
}{Earthquake
}\\
22 T & $
0.0027$ & $
0.9972$ \\
23 F & $
0.9973$ & $
0.0027$\\
27 \begin{tabular
}{|l|ll|
}
29 &
\multicolumn{2}{c|
}{Burglar
}\\
31 T & $
0.0027$ & $
0.9973$ \\
32 F & $
0.9973$ & $
0.0027$\\
36 \begin{tabular
}{|l|ll|
}
38 &
\multicolumn{2}{c|
}{$I_1$
}\\
45 \begin{tabular
}{|l|ll|
}
47 &
\multicolumn{2}{c|
}{$I_2$
}\\
54 \begin{tabular
}{|ll|ll|
}
56 &&
\multicolumn{2}{c|
}{Alarm
}\\
57 $I_1$ & $I_2$ & T & F\\
66 \begin{tabular
}{|l|ll|
}
68 &
\multicolumn{2}{c|
}{Watson
}\\
75 \begin{tabular
}{|l|ll|
}
77 &
\multicolumn{2}{c|
}{Gibbons
}\\
84 \begin{tabular
}{|l|ll|
}
86 &
\multicolumn{2}{c|
}{Radio
}\\
89 T & $
0.9998$ & $
0.0002$\\
90 F & $
0.0002$ & $
0.9998$\\