PHD ORAL PRESENTATION:
Hidden Markov models are a class of statistical models that are widely used in a variety of applications. Exact inference on these models is typically intractable when the model dynamics are nonlinear and non-Gaussian, and numerical methods must be employed instead. Particle filtering is a popular and powerful Monte Carlo method that is used in this context; it is also called sequential Monte Carlo. This talk consists of two parts. The first part is mainly methodological in which a framework for coupling particle filters is developed. Ideas from optimal transport literature are utilised to build an efficient coupled resampling step. Computationally-tractable approximations to optimal transport couplings are introduced to speed things up. The second part is mainly theoretical and concerns parallelising particle filters. A recent algorithm known as αSMC is considered and its time-uniform stability is related to the spectral gap of its underlying communication structure. An asymptotic analysis is also provided and it is proved that the αSMC algorithm can be asymptotically efficient even for extremely sparse communication structures.