An Axiomatic Framework for Bayesian and Belief-function Propagation
Prakash Shenoy, Glenn Shafer
In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.
PDF Link: /papers/88/p307-shenoy.pdf
AUTHOR = "Prakash Shenoy
and Glenn Shafer",
TITLE = "An Axiomatic Framework for Bayesian and Belief-function Propagation",
BOOKTITLE = "Proceedings of the Fourth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-88)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1988",
PAGES = "307--314"