Fully probabilistic knowledge expression and incorporation

Exploitation of prior knowledge in parameter estimation is vital whenever data is not informative enough. Elicitation and quantification of prior knowledge is a well-elaborated art in social and medical appliations but not in engineering ones. Frequently required involvment of a facilitator is mostly unrealistic due to either facilitators' high costs or the high complexitu of modelled relationships that cannot be grasped by the human. This paper provides a facilitator-free approach exploiting a methodology of knowledge sharing. The considered task assumes prospective models be indexed by an unknown finite-dimensional parameter. The parameter is estimated using (i) observed data; (ii) a prior probability density function (pdf); and (iii) uncertain expert's information on the modelled data. The parametric model specifies pdf of the system's output conditioned on realised data and parameter. Data is assumed to enter the time invariant-model only via a finite-dimensional regression vector. The adopted methodology deals with expert's knowledge expressed as a collection of pdfs on the space of data trajectories. Instead of sampling from these pdfs and applying Bayes rule to the samples, the proposed approach uses the asymptotic formulae arisen from Gedanken experiment relevant to the knowledge considered.