Bayesian estimation of incompletely observed diffusions

van der Meulen, F.H.; Schauer, M.R.

doi:10.1080/17442508.2017.1381097

Bayesian estimation of incompletely observed diffusions

Title

Bayesian estimation of incompletely observed diffusions

Author

van der Meulen, F.H. (TU Delft Statistics)
Schauer, M.R. (Universiteit Leiden)

Date

2017

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)).

Subject

Data augmentation
enlargement of filtration
filtered bridge
guided proposal
innovation scheme
Metropolis–Hastings
multidimensional diffusion bridge
partially observed diffusion
smoothing diffusion processes

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http://resolver.tudelft.nl/uuid:8722f716-8570-4656-beaa-14f3dc4072ef

DOI

https://doi.org/10.1080/17442508.2017.1381097

ISSN

1744-2508

Source

Stochastics: an international journal of probablitiy and stochastic processes, 90 (5), 641-662

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