  For many real-life Bayesian networks, common knowledge dictates that the
output established for the main variable of interest increases with higher
values for the observable variables. We define two concepts of monotonicity to
capture this type of knowledge. We say that a network is isotone in
distribution if the probability distribution computed for the output variable
given specific observations is stochastically dominated by any such
distribution given higher-ordered observations; a network is isotone in mode if
a probability distribution given higher observations has a higher mode. We show
that establishing whether a network exhibits any of these properties of
monotonicity is coNPPP-complete in general, and remains coNP-complete for
polytrees. We present an approximate algorithm for deciding whether a network
is monotone in distribution and illustrate its application to a real-life
network in oncology.
