Lattices for studying monotonicity of Bayesian networks

In many real problem domains, the main variable of interest behaves monotonically in terms of the observable variables, in the sense that higher values for the variable of interest become more likely with higher-ordered observations. Unfortunately, establishing whether or not a Bayesian network exhibits these monotonicity properties is highly intractable in general. In this paper, we present a method that, by building upon the concept of assignment lattice, provides for identifying any violations of the properties of (partial) monotonicity of the output and for constructing minimal oending contexts. We illustrate the application of our method with a real Bayesian network in veterinary science.