  The causal (belief) network is a well-known graphical structure for
representing independencies in a joint probability distribution. The exact
methods and the approximation methods, which perform probabilistic inference in
causal networks, often treat the conditional probabilities which are stored in
the network as certain values. However, if one takes either a subjectivistic or
a limiting frequency approach to probability, one can never be certain of
probability values. An algorithm for probabilistic inference should not only be
capable of reporting the inferred probabilities; it should also be capable of
reporting the uncertainty in these probabilities relative to the uncertainty in
the probabilities which are stored in the network. In section 2 of this paper a
method is given for determining the prior variances of the probabilities of all
the nodes. Section 3 contains an approximation method for determining the
variances in inferred probabilities.
