If the continuous nodes are always observed, it is trivial to handle
them using junction tree or variable elimination: the basic idea is to
delay evaluation of the conditional probability distributions (and hence
clique potentials) until the evidence arrives. This is explained in my
UAI 99 paper, "A variational approximation for bayesian networks with
discrete and continuous latent variables", section 8, and implemented in
my software, http://HTTP.CS.Berkeley.EDU/~murphyk/Bayes/bnt.html.
If the continuous nodes may be hidden, things become much more
complicated. If all the cts nodes are Gaussian and have no discrete
children, the network is called conditionally Gaussian, as others have
mentioned already. If a hidden Gaussian node has a discrete child, the
required integration cannot be performed in closed form (no matter
whether we use jtree or var. elim.). In my UAI 99 paper, I discuss a
variational approx. to this problem. Other approaches include
discretization, sampling and numerical integration (which is basically
clever discretization).
Kevin
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