Inference for a Random Wavelet Packet Model of Single-Channel Event-Related Potentials

Event-related potentials (ERPs) are brain electrical potentials associated with sensory and cognitive processing. ERP researchers typically wish to separate a recorded time series into functionally distinct component waveforms, and to estimate the effects of experimental conditions on each component. We present an integrated statistical approach to the decomposition of single-channel ERPs and to inference concerning the component waveforms and the effects of experimental conditions on the amplitude and latency (lag from stimulus presentation) of each component. A wavelet packet model of a single individual's data defines a unique decomposition based on prior time/frequency information and variation among experimental conditions. A particular orthogonal wavelet packet basis is selected using the best basis algorithm with a special cost function that incorporates prior information. Our statistical model allows individual-specific parameters to vary randomly among individuals. Because the number of observations on each individual is several orders of magnitude greater than the number of independent individuals, we fit our mixed model using a two-stage approach. In the first stage, a separate wavelet packet model is fit to each individual's data; in the second stage, the parameter estimates from the first stage are analyzed. We evaluated our method using numerical experiments based on design and analysis concepts that are common in applied statistics, but that are rarely used in evaluation of new statistical methods. We applied our methods to auditory evoked responses of cats recorded before and after lesions of the brain association cortex and at several stimulus rates. Our data analysis revealed a surprising lesion effect on the auditory brainstem response.