A basis function approach to Bayesian inference in diffusion processes

Yuan Shen, Dan Cornford, Manfred Opper

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationIEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09
PublisherIEEE
Pages365-368
Number of pages4
ISBN (Print)9781424427093
DOIs
Publication statusPublished - 2009

Fingerprint

Bayesian inference
Gaussian Process
Diffusion Process
Basis Functions
Approximation algorithms
State estimation
Moment Equations
Computational complexity
Ornstein-Uhlenbeck Process
Time Discretization
State Estimation
Approximation
Control Parameter
Smoothing
Approximation Algorithms
Continuous Time
Computational Complexity
Eliminate
Subspace

Bibliographical note

IEEE/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.

Keywords

  • Bayesian inference
  • continuous-time diffusion processes
  • variational Gaussian Process approximation
  • VGPA
  • Bayesian smoothing
  • partially observed diffusions
  • basis function expansion
  • BF-VGPA
  • time-dependent control parameters
  • GP process
  • moment equations
  • lower-dimensional subspace
  • Ornstein-Uhlenbeck process
  • BF-VGPA algorithm
  • state estimation

Cite this

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
Shen, Yuan ; Cornford, Dan ; Opper, Manfred. / A basis function approach to Bayesian inference in diffusion processes. IEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09. IEEE, 2009. pp. 365-368
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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. IEEE, pp. 365-368. https://doi.org/10.1109/SSP.2009.5278564

A basis function approach to Bayesian inference in diffusion processes. / Shen, Yuan; Cornford, Dan; Opper, Manfred.

IEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09. IEEE, 2009. p. 365-368.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Shen Y, Cornford D, Opper M. A basis function approach to Bayesian inference in diffusion processes. In IEEE/SP 15th Workshop on Statistical Signal Processing, 2009. SSP '09. IEEE. 2009. p. 365-368 https://doi.org/10.1109/SSP.2009.5278564