Stochastic ordering and robustness in classification from a Bayesian network

Consider a model-based decision support system where all the variables involved are binary, each taking on 0 or 1. The system categorizes the probability that a certain variable is equal to 1 conditional on a set of variables in an ascending order of the probability values and predicts for the variable in terms of category levels. Under the condition that all the variables are positively associated with each other, it is shown in this paper that the category levels are robust to the probability values. This robustness is illustrated by a simulated experiment using a variety of model structures where a set of probability values is proposed for a robust classification. A robust classification method is proposed as an alternative when exact or satisfactory probability values are not available.