  Dynamic trees are mixtures of tree structured belief networks. They solve
some of the problems of fixed tree networks at the cost of making exact
inference intractable. For this reason approximate methods such as sampling or
mean field approaches have been used. However, mean field approximations assume
a factorized distribution over node states. Such a distribution seems unlickely
in the posterior, as nodes are highly correlated in the prior. Here a
structured variational approach is used, where the posterior distribution over
the non-evidential nodes is itself approximated by a dynamic tree. It turns out
that this form can be used tractably and efficiently. The result is a set of
update rules which can propagate information through the network to obtain both
a full variational approximation, and the relevant marginals. The progagtion
rules are more efficient than the mean field approach and give noticeable
quantitative and qualitative improvement in the inference. The marginals
calculated give better approximations to the posterior than loopy propagation
on a small toy problem.
