Abstract

Motivated by applications in the development of decision support software for
emergency planning under uncertainty, we introduce a new framework for
probability propagation.  The hierarchical junction tree (HJT) provides a
platform for forecasting with Bayesian networks (BNs) for dynamic models with a
heterogeneous evolution, In this setting new descendant nodes need to be added
sequentially to the BN whilst nodes earlier in the BN are sequentially learned.
Interest focuses on the calculation of distributions of the most recently added
nodes given the observations so far.  Thus probability propagation is restricted
to calculation of a subset of the terminal nodes given a subset of their
ancestors.  
The junction tree provides a framework for computing distributions
of any set of variables given any other set of variables.  In the dynamic
setting this generality requires on-line triangulation:  hnown to be
computationally expensive.  The HJT preserves the time consistent edge direction
of the BN.  As a consequence, the HJT is constructed without conditional
independence loss when the ancestral graph of the conditioning variables is
decomposable.  If this is not the case, only the ancestral graph of the
conditioning variables needs to be triangulated.