Information and Statistical Structure in Spike Trains

One of the most challenging and fascinating problems in science is deciphering how neural systems encode information. Mathematical models are critical in any effort to determine how neural systems represent and transmit information. Such mathematical approaches span a wide range, which may be divided approximately into two kinds of research activities. The first kind of activity uses detailed biophysical models (e.g., Hodgkin–Huxley and its variants) of individual neurons, detailed biophysical models of networks of neurons, or artificial neural network models to study emergent behaviors of neural systems. The second kind of activity develops signal-processing algorithms to analyze the ever-growing volumes of data collected in neuroscience experiments. In an ideal scientific investigation there is a direct link between experiments and theoretical modeling. The theoretical models make predictions that can be used to guide experiments; the experiments provide data that allow for refinement (or rejection) of theoretical models. The growing complexity of neuroscience experiments makes use of appropriate data analysis methods crucial for establishing how reliably specific system properties can be identified from experimental measurements. Thus, careful data analysis is an essential complement to theoretical modeling. It allows validation of theoretical model predictions and provides biologically relevant constraints and parameter values for further analytic and simulation studies (see figure 1).