Bayesian probabilistic extensions of a deterministic classification model
SummaryThis 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 X1,...,Xk, a Boolean regression model is a conjunctive (or disjunctive) logical combination consisting of a subset S of the X variables, which predicts Y. Formally, Boolean regression models include a specification of a k-dimensional binary indicator vector (θ1,...,θk) with θj = 1 iff Xj∈S. In a probabilistic extension, a parameter π is added which represents the probability of the predicted value ŷi and the observed value yi differing (for any observation i). Within a Bayesian framework, a posterior distribution of the parameters (θl,...,θk, π) is looked for. The advantages of such a Bayesian approach include a proper account of the uncertainty in the model estimates and various possibilities for model checking (using posterior predictive checks). We illustrate this method with an example using real data.