25 Feb Chris Stanton - Particle-based Inference for Continuous-Discrete State Space Models скачать в хорошем качестве

25 Feb Chris Stanton - Particle-based Inference for Continuous-Discrete State Space Models

Talk given by Chris Stanton Title: Particle-based Inference for Continuous-Discrete State Space Models Abstract: We develop a methodology allowing application of the complete machinery of particle-based inference upon the class of continuous-discrete State Space Models (CD-SSMs). This class corresponds to a latent continuous-time diffusion observed with noise at discrete-time instances. Due to the continuous-time nature of the signal, standard Feynman-Kac formulations and their particle-based approximations have to overcome several challenges, including: (i) finite-time transition densities of the signal are typically intractable; (ii) ancestors of sampled signals are determined w.p.~1, thus cannot be resampled; (iii) diffusivity parameters given a sampled signal yield Dirac distributions. We overcome such issues by building a framework of carefully designed path proposals and reparameterisations thereof, and obtain new expressions for the Feynman-Kac model that accommodate the effects of continuous-time signals. Our formulations enable use of the full range of particle-based algorithms for CD-SSMs: for filtering/smoothing and parameter inference, online or offline. Our framework is compatible with guided proposals in the filtering steps which are essential for efficient performance under informative observations or in higher dimensions, and is applicable for a general class of CD-SSMs, including the case when the signal is a hypo-elliptic diffusion. We incorporate our methods into an established probabilistic programming package and present several numerical examples.