Bayesian Probabilistic Extensions of a Determin- Istic Classiication Model

This paper extends deterministic models for Boolean regression within a Bayesian framework. For a given binary criterion variable Y and a set of k binary predictor variables X 1 ; : : : ; X k , a Boolean regression model is a con-junctive (or disjunctive) logical combination consisting of a subset S of the X variables, which predicts Y. Formally, Boolean regression models include a speciication of a k-dimensional binary indicator vector (1 ; : : : ; k) with j = 1 ii X j 2 S. In a probabilistic extension, a parameter is added which represents the probability of the predicted value ^ y i and the observed value y i to diier (for any observation i). Within Bayesian estimation, a posterior distribution of the parameters (1 ; : : : ; k ;) is looked for. The advantages of such a Bayesian approach include a proper account for the uncertainty in the model estimates and various possibilities for model checking (using posterior predictive checks). We illustrate in an example using real data.