Models for integrate-and-fire neurons

Stochastic models of neural activity are a well developed application in biology. Diffusion models for integrate-and-fire neurons hold a prominent place because of the many synaptic inputs to a neuron, and because these models arise out of noisy versions of differential equations for the neural membrane's electrical properties. While the probabilistic aspects of such models have been well studied, inferential and computational procedures for them are not as well developed. In this talk, I outline the physiological background leading to these models. I then describe recent progress in parameter estimation and the computational problems that arise. I will also describe some exploratory graphical methods for the analysis of data from multiple neurons.