Bayesian estimation of incompletely observed diffusions

Journal article (2017)

Authors

F.H. van der Meulen Statistics - EEMCS
M.R. Schauer Universiteit Leiden
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2017 F.H. van der Meulen, M.R. Schauer
DOI: https://doi.org/10.1080/17442508.2017.1381097
Data augmentation Enlargement of filtration Filtered bridge Guided proposal Innovation scheme Metropolis–Hastings Multidimensional diffusion bridge Partially observed diffusion Smoothing diffusion processes
More Info
expand_more

Published Date

2017

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)).