Monte Carlo algorithms for performing Bayesian inference on Piecewise Deterministic Processes

Abstract

Since their introduction in 1993, particle filters are amongst the most popular algorithms for performing Bayesian inference on state space models that do not admit an analytical solution. In this thesis, we will present several particle filtering algorithms adapted to a class of models known as Piecewise Deterministic Markov Processes (PDMP), i.e. processes governed by one or more parameters that admit random jumps in their value at random times. Our work will focus on object tracking, the estimation of a target’s kinematic state over time from a sequence of noisy or incomplete measurements. Moreover, we will combine these techniques with Markov Chain Monte Carlo methods in order to infer the model parameters. We will perform sequential inference on both parameters and states by introducing an adaptation of the SMC2 to PDMPs. Finally, all algorithms will be tested both on simulated and real-world data (Piraeus AIS Dataset).