BAYESIAN REGRESSION FILTERS AND THE ISSUE OF PRIORS

We propose a Bayesian framework for regression problems, which covers areas usually dealt with by function approximation. An online learning algorithm is derived which solves regression problems with a Kalman f ilter. its solution always improves with increasing model complexity, without the risk of over-fitting. In the infinite dimension limit it a pproaches the hue Bayesian posterior. The issues of prior selection an d over-fitting are also discussed, showing that some of the commonly h eld beliefs are misleading. The practical implementation is summarised . Simulations using 13 popular publicly available data sets are used t o demonstrate the method and highlight important issues concerning the choice of priors.