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.