Summary: We explore a Bayesian framework for constructing combinations of classifier outputs, as a means to improving overall classification results. We propose a sequential Bayesian framework to estimate the posterior probability of being in a certain class given multiple classifiers. This framework, which employs meta-Gaussian modelling but makes no assumptions about the distribution of classifier outputs, allows us to capture nonlinear dependencies between the combined classifiers and individuals. An important property of our method is that it produces a combined classifier that dominates the individuals upon which it is based in terms of Bayes risk, error rate, and receiver operating characteristic (ROC) curve. To illustrate the method, we show empirical results from the combination of credit scores generated from four different scoring models.