Bayesian estimation of incompletely observed diffusions

Frank van der Meulen, Moritz Schauer

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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)).

Original languageEnglish
Pages (from-to)641-662
Number of pages22
JournalStochastics: an international journal of probablitiy and stochastic processes
Volume90
Issue number5
DOIs
Publication statusE-pub ahead of print - 2017

Keywords

  • 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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