Optimized geometric pooling of probabilities for information fusion and forgetting

Geometric pooling of probability densities (pd) is an old but basic technique of the fusion of probabilistic knowledge. Among its many justification, the use of the axiomatic minimum relative entropy principle (MREP) is the simplest one. Up to now, however, the common choice of the pooling weights is unavailable. It is done by a range of techniques. Mostly, they are of a heuristic nature and often interpret the weights as a relative trust. This paper shows that the full rigorous use of MREP enables quantitative choice of the weights, too. It quantifies the trust while using just the properly interpreted knowledge, which is deductively processed. The geometric pooling serves well adaptive estimation with forgetting that suits for illustration of our result. The paper presents an adaptive Bayesian estimator with the restricted stabilized forgetting.