Bayesian estimation of incompletely observed diffusions

TL;DR

This paper introduces a Bayesian framework for estimating multivariate diffusion processes with incomplete, noisy, and discrete observations, utilizing a data-augmentation algorithm based on simulating diffusion bridges.

Contribution

It develops a novel data-augmentation algorithm for Bayesian inference in incomplete diffusion models using guided proposals for simulating diffusion bridges.

Findings

Effective posterior sampling for incomplete diffusion data

Extension of guided proposals to noisy, incomplete observations

Framework applicable to multivariate diffusion processes

Abstract

We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time. The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer et al. (2016).