This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon sequential Monte Carlo methods, investigating the problems of...

We develop particle Gibbs samplers for static-parameter estimation in discretely observed piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. A sequential Monte...

The majority of modelling and inference regarding Hidden Markov Models (HMMs) assumes that the number of underlying states is known a priori. However, this is often not the case and thus determining the appropriate number of underlying states for a HMM is of considerable interest. This paper...