Point process theory: a framework for analysis of neural information encoding

Emery N. Brown


The theory of point processes is a well developed field of probability and stochastic processes that has received limited application in the analysis of neural spike train data and neural information encoding. Central to this approach is the characterization of joint probability density of a spike train in terms of the conditional intensity function. The conditional intensity extends the definition of the Poisson rate function to that of a rate function for a general point process. Once specified, the conditional intensity provides a canonical representation of the spike train, i.e. it completely describes the stochastic structure of the spike train and its dependence on system history. The power of the point process theory is that it provides a framework for not only theoretical analysis of neural systems but also for constructing methods for neural spike train data analysis.

We use the well-known canonical representation of point processes in terms of the conditional intensity (generalized rate) function to describe a paradigm for analyzing spike train data. First, we review briefly the relevant results from point process theory needed to develop statistical models of rat hippocampal place cell neurons recorded during spatial behavioral tasks. Second, we present goodness-of-fit techniques for these models based on the time-rescaling theorem. The time-rescaling theorem is a powerful result, which states that any point process can be rescaled into a Poisson process via its conditional intensity. We use these goodness-of-fit techniques to assess how well our statistical models describe individual place cell spiking activity. Third, we show that the conditional intensity characterization leads naturally to population decoding algorithms based on the Chapman-Kolmogorov equations. We quantify from these decoding algorithms in terms of either coverage probabilities or Shannon information the extent to which improved descriptions of individual place cell spiking activity yield better descriptions of the ensemble representation of place and trajectories. Fourth, the place receptive fields of hippocampal neurons are dynamic, i.e. the fields evolve over the course of an experiment even when the animal is in a familiar environment. We present an adaptive estimation algorithm based on the conditional intensity function to track in real-time the spatio-temporal dynamics of place field evolution. Point process theory provides a solid framework for the methods we are developing to understand the role of rat hippocampal neurons in spatial information encoding.