Uncertainty and filtering of hidden Markov models in discrete time

TL;DR

This paper addresses filtering hidden Markov models with uncertain parameters using nonlinear expectations, proposing a method to propagate uncertainty through a penalty function instead of traditional filtering techniques.

Contribution

It introduces a novel approach to handle parameter uncertainty in hidden Markov models by employing nonlinear expectations and penalty functions.

Findings

Provides a framework for uncertainty propagation in HMM filtering.

Demonstrates the use of penalty functions as an alternative to traditional filters.

Enhances robustness of filtering under model uncertainty.

Abstract

We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty in terms of a penalty function, which can be propagated forward in time in the place of the filter.