Bayesian estimation of filtered point processes using Markov chain Monte Carlo methods

Filtered point processes model a huge amount of physical phenomena. Usually, only noisy observations are in practice available. From these data, one would like to estimate the parameters of the filtered point process. This is a complex problem which in general does not admit any closed-form solution. In this paper, we propose stochastic algorithms to perform statistical estimation for such processes in a Bayesian framework. These algorithms rely on Markov chain Monte Carlo methods which are powerful stochastic simulation methods.