Robert E. Kass, Carnegie Mellon University

Bayesian Curve Fitting and Neuronal Firing Patterns

A central problem in cognitive neuroscience is to understand the way neuronal firing patterns represent information---this is usually discussed under the rubric of ``neural coding.'' From a statistical point of view, the issues involved have to do with the analysis of single and multiple point process data. Together with colleagues in our Department and at the joint Carnegie Mellon and University of Pittsburgh Center for the Neural Basis of Cognition, I have been working on spline-based methods of fitting inhomogeneous Poisson processes, and a non-Poisson generalization of these, to single and multiple neuron data. In my talk, I will briefly describe the neurophysiological setting, and some results using standard smoothing methods, and then use this as a background to discuss a general approach to curve fitting with free-knot splines and reversible-jump Markov chain Monte Carlo. Simulation results indicate this to be a powerful methodology. I will introduce it in the setting of Normal observations, then show how it may be applied to Poisson and other non-Normal data, so that we will ultimately arrive at a fairly general approach to fitting neuronal ``spike train'' point process intensity functions.