Bayesian methods for adaptive models

The Bayesian framework for model comparison and regularisation is demonstrated by studying interpolation and classification problems modelled with both linear and non-linear models. This framework quantitatively embodies `Occams razor. Over-complex and under-regularised models are automatically inferred to be less probable, even though their flexibility allows them to fit the data better. When applied to `neural networks, the Bayesian framework makes possible (1) objective comparison of solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of type of weight decay terms (or regularisers); (4) on--line techniques for optimising weight decay (or regularisation constant) magnitude; (5) a measure of the effective number of well--determined parameters in a model; (6) quantified estimates of the error bars on network parameters and on network output. In the case of classification models, it is sho...