  In a Bayesian network, we wish to evaluate the marginal probability of a
query variable, which may be conditioned on the observed values of some
evidence variables. Here we first present our "border algorithm," which
converts a BN into a directed chain. For the polytrees, we then present in
details, with some modifications and within the border algorithm framework, the
"revised polytree algorithm" by Peot & Shachter (1991). Finally, we present our
"parentless polytree method," which, coupled with the border algorithm,
converts any Bayesian network into a polytree, rendering the complexity of our
inferences independent of the size of network, and linear with the number of
its evidence and query variables. All quantities in this paper have
probabilistic interpretations.

Artificial Intelligence