Bayesian data assimilation based on a family of outer measures

TL;DR

This paper introduces a novel outer measure-based framework for data assimilation that combines additive and sub-additive components, enabling more flexible uncertainty representation within probabilistic measure theory.

Contribution

It presents a new family of outer measures for data assimilation, expanding the theoretical tools available for uncertainty modeling.

Findings

Enables intuitive pullback and data assimilation operations

Combines additive and sub-additive measure components

Provides a flexible uncertainty representation within measure theory

Abstract

A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is based on the measure of a supremum, hence combining additive and highly sub-additive components. It is shown that this type of outer measure enables the introduction of intuitive concepts such as pullback and general data assimilation operations.