  We show an alternative way of representing a Bayesian belief network by
sensitivities and probability distributions. This representation is equivalent
to the traditional representation by conditional probabilities, but makes
dependencies between nodes apparent and intuitively easy to understand. We also
propose a QR matrix representation for the sensitivities and/or conditional
probabilities which is more efficient, in both memory requirements and
computational speed, than the traditional representation for computer-based
implementations of probabilistic inference. We use sensitivities to show that
for a certain class of binary networks, the computation time for approximate
probabilistic inference with any positive upper bound on the error of the
result is independent of the size of the network. Finally, as an alternative to
traditional algorithms that use conditional probabilities, we describe an exact
algorithm for probabilistic inference that uses the QR-representation for
sensitivities and updates probability distributions of nodes in a network
according to messages from the neighbors.
