A Probabilistic Approach to Optimal Estimation Part I: Problem Formulation and Methodology

The focal point of this paper is to provide a rapproachement between these two paradigms and propose a novel probabilistic framework for system identification. The main idea in this line of research is to "discard" sets of measure at most epsilon, where epsilon is a probabilistic accuracy, from the set of deterministic estimates. Therefore, we are decreasing the so-called worst-case radius of information at the expense of a given probabilistic "risk."