Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods

作者: Martin Hairer , A. M. Stuart , J. Voss

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摘要: In this chapter we overview a Bayesian approach to wide range of signal processing problems in which the goal is find signal, solution an ordinary or stochastic differential equation, given noisy observations its solution. case equations (ODEs) gives rise finite dimensional probability measure for initial condition, then determines on signal. (SDEs) infinite dimensional, itself, time-dependent SDE. We derive posterior these problems, applying ideas ODEs and SDEs, with discrete continuous observations, coloured white noise. highlight common structure inherent all namely that absolutely respect Gaussian prior. This leads naturally study Langevin are invariant theory open questions relating S(P)DEs. describe construction effective Metropolis-based sampling methods measure, based proposals can be interpreted as approximations equation.