Assimilating data with outer probability measures

Although using probability distributions to model uncertainty is by far the most widely accepted approach, it does not come without inconveniences. A basic example of such shortcomings is the inability to represent the absence of information in general, which creates a gap between Bayesian and frequentist methods and which motivated the introduction of workarounds like improper priors. Many other representations of uncertainty were developed through the years, starting with Fisher's fiducial inference, but none has yet become a viable alternative to the standard approach. This talk will focus on a recent attempt at generalising probability distributions, based on the concept of outer measure, and explain how it allows for representing both random and deterministic uncertainty. This approach also strengthen the links between Bayesian and frequentist methods and further connects inference and optimisation. Illustrations will be given for different data assimilation problems.

Invited by Jana de Wiljes