next up previous
Next: Beta distribution [2 P] Up: MLA_Exercises_2009 Previous: d-separation II [3 P]

Bayesian Networks [2+1* P]

Figure: Three possible networks for the telescope problem.
\includegraphics[width=12cm]{./1419.eps}
Two astronomers in different parts of the world make measurements $ M1$ and $ M2$ of the number of stars $ N$ in some small region of the sky, using their telescopes. Normally, there is a small possibility $ e$ of error by up to one star in each direction. Each telescope can also (with a smaller probability $ f$ ) be badly out of focus (events $ F1$ and $ F2$ ), in which case the scientists will undercount by three or more stars (or, if $ N$ is less than 3, fail to detect any stars at all). Consider the three networks illustrated in Figure 2.

a)
[1 P] Which of these Bayesian networks are correct (but not necessarily efficient) representations of the preceding information?
b)
[1* P] Which is the best network? Why?
c)
[1 P] Write out a conditional distribution for $ P(M1\vert N)$ , for the case $ N \in \{1,2,3\}$ and $ M1 \in \{0,1,2,3,4\}$ . Each entry in the conditional distribution should be expressed as a function of the parameters $ e$ and/or $ f$ .


next up previous
Next: Beta distribution [2 P] Up: MLA_Exercises_2009 Previous: d-separation II [3 P]
Haeusler Stefan 2010-01-26