Stochastic ordering and robustness in classification from a Bayesian network

Consider a model whose structure is representable via recursive graph or Bayes network and in which both observable and unobservable variables are involved. Assume that the variables are all binary and suppose that we want to predict about the unobservables based on the evidence from the observables. In the real world, we may not be able construct a model that exactly explains a certain phenomenon we are interested in. However, if we may give predictions in terms of class or category rather than probability, then we may not have to know the exact details of the model. It is shown in this article that when the observables are conditionally independent and conditionally stochastically ordered given the unobservables, the unobservables are conditionally ordered given the observables. This result suggests to some extent robustness of the conditional probabilities of the observables given the unobservables, and the simulation result strongly supports the suggestion.