Via Zoom: A Theory of Uncertainty Variables for State Estimation and Inference

Rajat will discuss a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by a set in which its realization is bound to lie. Conditional uncertainty, on the other hand, is characterized by a set-map, from a given realization of one variable to a set of possible realizations of another. We prove Bayes’ law and the law of total probability equivalents for uncertainty variables. We extend the notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence as we know them for random variables. We also develop graphical models over a collection of uncertainty variables and show that the expected conditional independence properties continue to hold true.

Reference: Rajat Talak, Sertac Karaman, and Eytan Modiano "A Theory of Uncertainty Variables for State Estimation and Inference" Allerton 2019.