Many of the experimental non-invasive brain imaging techniques measure the collective behaviour of millions of neurons. It therefore makes sense to model at the population level, rather than to simulate networks of individual neurons. Recently, Knight et al. (1996) proposed a statistical description of a neural population in the form of a PDE which describes the evolution of a probability distribution function over membrane potentials in the population. All properties of the population, in particular its output firing rate in response to input can be derived from the density function.
Solving the PDE is in general much more efficient than Monte Carlo simulations of the population. In this talk I will discuss a solution method that 'transforms away' the neuronal dynamics, which leads to a version of the master equation of a Poisson process that can be solved analytically. The result is a very fast and stable algorithm, although there are some numerical problems that need to be addressed.