Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

TL;DR

This paper develops Bayesian inference methods for partially observed fractional Brownian motion models, introducing a novel discretization and multilevel MCMC to efficiently estimate parameters from data.

Contribution

It presents a new discretization approach combined with importance sampling and multilevel MCMC for efficient Bayesian inference in fractional Brownian motion models.

Findings

The proposed method reduces computational cost compared to traditional approaches.

The approach is effective on both simulated and real data.

Multilevel MCMC improves accuracy versus single discretization.

Abstract

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling; the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data.