Bayesian estimation of incompletely observed diffusions

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).

References in corpus (3)

• Simple simulation of diffusion bridges with application to likelihood inference for diffusions
• Guided proposals for simulating multi-dimensional diffusion bridges
• Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals

Cited by in corpus (5)

• Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals
• Continuous-discrete smoothing of diffusions
• Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes
• Simulation of elliptic and hypo-elliptic conditional diffusions
• Unbiased Estimation of the Hessian for Partially Observed Diffusions