Point-process filter

A point-process filter is a recursive Bayesian decoder whose observations are the spike trains themselves, modelled as a point process rather than binned rates. Instead of a Gaussian measurement equation it uses a conditional intensity function — the instantaneous firing probability of each neuron as a function of the hidden state and possibly spike history — as the observation likelihood. At each small time step the filter predicts the state forward and updates it using whether or not each neuron fired, typically keeping a Gaussian approximation to the posterior (the stochastic state point-process filter).

This formulation uses precise spike timing and does not force a bin width, which is advantageous when firing is sparse, non-stationary, or when a Gaussian rate approximation is poor. It was developed for decoding hippocampal position from place cells and is applied to motor and other BMI settings. The main costs are that it requires an explicit encoding model (the conditional intensity), inherits any misspecification of that model, and, in its common Gaussian-posterior form, is still an approximation to the exact spike-driven Bayesian filter.