Continuous-time estimation of latent variables from Poisson-spiking neurons

Online estimation of latent variables from neural firing patterns is important for interpretation of micro-electrode recordings and for brain-computer interfaces. Typical implementations require counting spikes over a fixed time-bin or low-pass filtering of the spike timeseries. Here we present a partial-differential equation that provides a continuous-time, low latency, Bayes-optimal estimate of the probability density of an underlying latent variable based on the spike train from one or more neurons with known tuning curves.