In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.
Bibliographical noteIEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09, 31 August - 4 Sept 2009, Cardiff (UK). © 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
- Bayesian inference
- continuous-time diffusion processes
- variational Gaussian Process approximation
- Bayesian smoothing
- partially observed diffusions
- basis function expansion
- time-dependent control parameters
- GP process
- moment equations
- lower-dimensional subspace
- Ornstein-Uhlenbeck process
- BF-VGPA algorithm
- state estimation
Shen, Y., Cornford, D., & Opper, M. (2009). A basis function approach to Bayesian inference in diffusion processes. In IEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09 (pp. 365-368). IEEE. https://doi.org/10.1109/SSP.2009.5278564