Bayesian Nonparametric Dynamic State Space Modeling with Circular Latent States

TL;DR

This paper introduces a Bayesian nonparametric state space model that captures dynamic systems with circular latent states, using Gaussian processes and MCMC for inference, demonstrated on real and simulated data.

Contribution

It proposes a novel Bayesian nonparametric framework for state space modeling with circular latent states, combining Gaussian processes and MCMC inference methods.

Findings

Effective modeling of circular latent states in dynamic systems

Successful application to wind speed and ozone data sets

Encouraging performance compared to traditional methods

Abstract

State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in comparison. In this article we propose a novel Bayesian nonparametric approach to state space modeling assuming that both the observational and evolutionary functions are unknown and are varying with time; crucially, we assume that the unknown evolutionary equation describes dynamic evolution of some latent circular random variable. Based on appropriate kernel convolution of the standard Wiener process we model the time-varying observational and evolutionary functions as suitable Gaussian processes that take both linear and circular variables as arguments. Additionally, for the time-varying evolutionary function, we wrap the Gaussian process thus constructed around the unit circle to form an appropriate circular Gaussian process. We show that our process thus created satisfies desirable properties. For the purpose of inference we develop an MCMC based methodology combining Gibbs sampling and Metropolis-Hastings algorithms. Applications to a simulated data set, a real wind speed data set and a real ozone data set demonstrated quite encouraging performances of our model and methodologies.