Application of penalized splines in analyzing neuronal data

Neuron experiments produce high-dimensional data structures. Therefore, application of smoothing techniques in the analysis of neuronal data from electrophysiological experiments has received considerable attention of late. We investigate the use of penalized splines in the analysis of neuronal data. This is first illustrated when interested in the temporal trend of a single neuron. An approach to investigate the maximal firing rate, based on the penalizedspline model is proposed. Determination of the time of maximal firing rate is based on non-linear optimization of the objective function with the corresponding confidence intervals constructed based on the first-order derivative function. To distinguish between the curves from different experimental conditions in a moment-by-moment sense, bias adjusted simulation-based simultaneous confidence bands leading to global inference in the time domain are constructed. The bands are an extension of the approach proposed by Ruppert et al. (2003). These methods are in a second step extended towards the analysis of a population of neurons via a marginal or population-averaged model.