Modeling heterogeneity and dependence for analysis of neuronal data.

In this paper, we describe two types of neuroscience problems which challenge the typical statistical models assumed for analyzing neuronal data. This offers an opportunity for new modeling and statistical inference. In the first problem, the data are spatial neural counts which are often over-dispersed and spatially correlated so that a standard Poisson regression model is inadequate. In the second problem, the data are averaged electroencephalograph signals recorded during muscle fatigue, where a time series AR(1) regression model cannot fully capture all the variation and correlation structure in the data. It is shown that an additional parameter has to be included in the modeling of the correlation structure and that the role of the parameter differs from one channel to the other. We propose appropriate generalized models for these data, develop statistical procedures under the generalized models, and apply these procedures to the real data that motivated this paper. The effect of mis-specification of a correlation structure is also investigated.