On the Collaboration Between Bayesian and Hilbertian Approaches

In this work, we explore the use of Uncertainty Quantification (UQ) techniques of representation in Bayes estimation and representation. UQ representation is a Hilbertian approach which furnishes distributions from experimental data in limited number. It can be used to generate priors to be used by Bayesian procedures. In a first use, we consider De Finetti’s representation theorem with few data points and we show that the UQ methods can furnish interesting priors, able to reproduce the correct distributions when integrated in the De Finetti’s representation theorem. In a second use, we consider Bayes estimation of the parameters of a distribution. Analogously to the preceding situation, a limited sample is used to generate a UQ representation of the parameters. Then, we use it as prior for the Bayesian procedure. The results show that the approach improves the quality of the estimation, when compared to the standard Bayesian procedure. The results are also compared to Fisher’s procedure of estimation.