  We begin with a review of a well known class of networks, Classical Bayesian
(CB) nets (also called causal probabilistic nets by some). Given a situation
which includes randomness, CB nets are used to calculate the probabilities of
various hypotheses about the situation, conditioned on the available evidence.
We introduce a new class of networks, which we call Quantum Bayesian (QB) nets,
that generalize CB nets to the quantum mechanical regime. We explain how to use
QB nets to calculate quantum mechanical conditional probabilities (in case of
either sharp or fuzzy observations), and discuss the connection of QB nets to
Feynman Path integrals. We give examples of QB nets that involve a single
spin-half particle passing through a configuration of two or three
Stern-Gerlach magnets. For the examples given, we present the numerical values
of various conditional probabilities, as calculated by a general computer
program especially written for this purpose.
