On the statistics of binned neural point processes: the Bernoulli approximation and AR representation of the PST histogram

Abstract

Neural point processes are often approximated by partitioning time into bins, each with a Bernoulli distribution of firing, in order to simplify the mathematical description of their properties. Some of the basic statistics of a neural process are compared using the Bernoulli approximation and the actual Poisson representation. It is seen that in general the Bernoulli approximation is an accurate model only for small λΔ where λ is the intensity and Δ is the width of the time bin. This discrete representation leads to a model of the PST histogram as an AR system, where the parameters depend upon the driving signal s(t) , the refractory effect r(t) and the binwidth Δ . This AR representation is used to predict the PST histogram given s(t) , r(t) and Δ . Estimates of s(t) and r(t) are derived within this parameterization and results discussed for several types of recovery functions given a constant s(t) . AR techniques are used to estimate the AR parameters from the PST histogram of a simulated point process, from which both s(t) and r(t) are estimated.