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Bayesian Inference for Diffusions using Data Augmentation MCMC

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Diffusion driven models provide natural models for phenomena evolving continuously in time. They appear quite often in various applications across a wide range of diverse scientific areas. The task of likelihood based inference for their parameters is particularly challenging as their infinite dimensional paths can only be observed at a finite number of points and the marginal likelihood for these observations is generally intractable. Things are further complicated by the presence of various observation regimes: the observations may be noisy, partial, from multiple potentially conflicting sources of information, they may correspond to functionals of the diffusion etc. Data augmentation schemes, implemented through MCMC , provide a general unified framework that may in theory handle all such cases. However, extra care is required because usually a suitable reparametrisation is needed to avoid degenerate MCMC algorithms. This talk presents the main features of this framework and illustrates the methodology through various examples.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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