Optimization and model averaging of histogram-based place cell firing rate maps using the point process framework

The firing rate of hippocampal place cells depends on the spatial position of the organism in an environment. This position dependence is often quantified by constructing spike-in-location and time-in-location histograms, the ratio of which yields a firing rate map. The purpose of this study is to present a new method for optimizing the spatial resolution of histogram-based firing rate maps. It is pointed out that histogram-based firing rate maps are conditional intensity functions of inhomogeneous Poisson process models of neural spike trains, and, as such, they can be optimized through model selection within the point process framework. The point process framework is used here for optimizing the size and the aspect ratio of the histogram bins using the Akaike Information Criterion (AIC). It is also used for model averaging using Akaike weights, when maps of various bin sizes provide comparable fits. Application of the method is illustrated on data from real rat hippocampal place cells. Existing methods do not optimize the number of bins used in each dimension of the firing rate map. The proposed approach allows for the construction of the AIC-best histogram-based firing rate map for each individual place cell.