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Previously, Bayesian methods have been proposed for neural networks to solve regression and classification problems. These methods claim to overcome some difficulties encountered in the standard approach such as overfitting. However, an implementation of the full Bayesian approach to neural networks as suggested in the literature applied to classification problems is not easy. In fact we are not aware of applications of the full approach to real world classification problems. In this paper we discuss how the Bayesian framework can improve the predictive performance of neural networks. We demonstrate the effects of this approach by an implementation of the full Bayesian framework applied to two real world classification problems. We also discuss the idea of calibration to measure the predictive performance.