A Monte Carlo sequential estimation for point process optimum filtering

Abstract — Adaptive filtering is normally utilized to estimate system states or outputs from continuous valued observations, and it is of limited use when the observations are discrete events. Recently a Bayesian approach to reconstruct the state from the discrete point observations has been proposed. However, it assumes the posterior density of the state given the observations is Gaussian distributed, which is in general restrictive. We propose a Monte Carlo sequential estimation methodology to estimate directly the posterior density. Sample observations are generated at each time to recursively evaluate the posterior density more accurately. The state estimation is obtained easily by collapse, i.e. by smoothing the posterior density with Gaussian kernels to estimate its mean. The algorithm is tested in a simulated neural spike train decoding experiment and re-constructs better the velocity when compared with point process adaptive filtering algorithm with the Gaussian assumption. I