Statistical modeling of neural spike train data

The advance of the multi-electrode has made the field of neural science feasible to record spike trains simultaneously from an ensemble of neurons. However, the statistical techniques for analyzing large-scale simultaneously recorded spike train data have not developed as satisfactorily as the experimental techniques for obtaining these data. This chapter describes a very flexible statistical procedure for modeling an ensemble of neural spike trains, followed with the associated estimation method for making an inference for the functional connectivity based on the statistical results. To

processes activities from noncholinergic basal forebrain neurons [11]. The formulation is equipped with the likelihood (or loosely, the probability) of the occurrence of the neural spike train data, based on which the statistical estimation and inference will be carried out. The model can assess the association or correlation between a target neuron and its peers.

1.1 INTRODUCTION It is known that neurons, even when they are apart in the brain, often exhibit correlated firing patterns [22]. For instance, coordinated interaction among cortical neurons is known to play an indispensable role in mediating many complex brain functions with highly intricate network structures [23]. A procedure to examine the underlying connectivity between neurons can be stated in the following way. For a target neuron i in a population of N observed neurons, we need to identify a subset of neurons that affect the firing of the target in some statistical sense.