Fast Bayesian Inference with Piecewise Deterministic Markov Processes - Hammar, Karl (My University, 2023)
Piecewise Deterministic Markov Processes (PDMPs) present a recent class of samplers for Bayesian inference. In this thesis, PDMP samplers are employed to sample state and latent parameters of an adversarial missile, described by an SDE. An approximate method for fast sampling is developed for this problem, and the performance of two different PDMP samplers, the Zig-Zag sampler, and the bouncy particle sampler, are compared. We find that the approximations needed for the methods to be competitive have a small impact on accuracy and that the method has the potential to be useful in real-world applications. Additionally, an approach for sampling from target models which may experience discontinuous jumps is developed. Using a particular trajectory realization of one such model we show that the method works as expected. This bears importance for the sampling of parameters related to maneuvering target types, where jump dynamics are relevant for target modeling.
Keywords: Bayesian inference, Stochastic process, Piecewise Deterministic Markov Process, State estimation.