A Stochastic Framework for Hybrid System Identification with Application to Neurophysiological Systems

This paper adapts the Gibbs sampling method to the problem of hybrid system identification. We define a Generalized Linear Hiddenl Markov Model (GLHMM) that combines switching dynamics from Hidden Markov Models, with a Generalized Linear Model (GLM) to govern the continuous dynamics. This class of models, which includes conventional ARX models as a special case, is particularly well suited to this identification approach. Our use of GLMs is also driven by potential applications of this approach to the field of neural prosthetics, where neural Poisson-GLMs can model neural firing behavior. The paper gives a concrete algorithm for identification, and an example motivated by neuroprosthetic considerations.