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Figure:
Three possible networks for the telescope problem.
|
Two astronomers in different parts of the world make measurements
and
of the number of stars
in some small region of the sky, using their telescopes. Normally, there is a small possibility
of error by up to one star in each direction. Each telescope can also (with a smaller probability
) be badly out of focus (events
and
), in which case the scientists will undercount by three or more stars (or, if
is less than 3, fail to detect any stars at all). Consider the three networks illustrated in Figure 1.
- 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
, for the case
and
. Each entry in the conditional distribution should be expressed as a function of the parameters
and/or
.
Next: d-separation [4+1* P]
Up: MLA_Exercises_2011
Previous: Conditional Independence II [2+1*
Haeusler Stefan
2011-12-06