Sequential Bayesian inference for implicit hidden Markov models and current limitations

TL;DR

This paper reviews recent advances in sequential Bayesian inference for hidden Markov models, highlighting current limitations in scalability, complexity, and flexibility, especially for long and high-dimensional data.

Contribution

It summarizes recent developments in incorporating parameter and model uncertainty into HMM inference and discusses the algorithmic challenges and open problems.

Findings

Recent methods include parameter and model uncertainty

Algorithmic complexity limits scalability to large data

Open challenges remain for high-dimensional models

Abstract

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.