| Summary: | Given evidence on a set of variables in a Bayesian network,
the most probable explanation (MPE) is the problem of nding a con guration
of the remaining variables with maximum posterior probability.
This problem has previously been addressed for discrete Bayesian networks
and can be solved using inference methods similar to those used
for finding posterior probabilities. However, when dealing with hybrid
Bayesian networks, such as conditional linear Gaussian (CLG) networks,
the MPE problem has only received little attention. In this paper, we provide
insights into the general problem of fi nding an MPE con guration in
a CLG network. For solving this problem, we devise an algorithm based
on bucket elimination and with the same computational complexity as
that of calculating posterior marginals in a CLG network. We illustrate
the workings of the algorithm using a detailed numerical example, and
discuss possible extensions of the algorithm for handling the more general
problem of fi nding a maximum a posteriori hypothesis (MAP).
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