Variable exponential forgetting for estimation of the statistics of the normal-Wishart distribution with a constant precision

The problem of estimating normal regression-type models with possibly time-varying regression parameters and constant noise precision is considered and examined from the Bayesian viewpoint. The solution we propose exploits a collaborative decision in order to face the incomplete model of parameter variations. Under this approach, a loss functional evaluating two prediction alternatives is constructed, which allows us to merge both alternatives, complying with the principles of optimization theory. Specifically, the posterior probability density function (pdf) and its flattened variant are combined by means of the geometric mean with automatically
adjusted weights. The result is an automatic rescaling of the covariance matrix through the forgetting factor in response to empirically confirmed performance.