Monte Carlo filtering of piecewise deterministic processes

We present efficient Monte Carlo algorithms for performing Bayesian inference in a broad class of models: those in which the distributions of interest may be represented by time marginals of continuous-time jump processes conditional on a realization of some noisy observation sequence. The sequential nature of the proposed algorithm makes it particularly suitable for online estimation in time series. We demonstrate that two existing schemes can be interpreted as particular cases of the proposed method. Results are provided which illustrate significant performance improvements relative to existing methods.