Bayesian estimation of incompletely observed diffusions. (English) Zbl 1500.60051
Summary: 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
[M. Schauer et al., Bernoulli 23, No. 4A, 2917–2950 (2017; Zbl 1415.65022)].
Keywords:
data augmentation; enlargement of filtration; guided proposal; filtered bridge; smoothing diffusion processes; innovation scheme; Metropolis-Hastings; multidimensional diffusion bridge; partially observed diffusionCitations:
Zbl 1415.65022References:
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