Bayesian approach for neural networks—review and case studies

We give a short review on the Bayesian approach for neural network learning and demonstrate the advantages of the approach in three real applications. We discuss the Bayesian approach with emphasis on the role of prior knowledge in Bayesian models and in classical error minimization approaches. The generalization capability of a statistical model, classical or Bayesian, is ultimately based on the prior assumptions. The Bayesian approach permits propagation of uncertainty in quantities which are unknown to other assumptions in the model, which may be more generally valid or easier to guess in the problem. The case problem studied in this paper include a regression, a classification, and an inverse problem. In the most thoroughly analyzed regression problem, the best models were those with less restrictive priors. This emphasizes the major advantage of the Bayesian approach, that we are not forced to guess attributes that are unknown, such as the number of degrees of freedom in the model, non-linearity of the model with respect to each input variable, or the exact form for the distribution of the model residuals.