Multimodal diffusion model for increments of electroencephalogram data

Abstract

AbstractWe propose a new strictly stationary strong mixing diffusion model with marginal multimodal (three-peak) distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram data collected from Ugandan children during coma from cerebral malaria. We treat the increments as discrete-time observations and construct a diffusion process where the stationary distribution is viewed as a mixture of three non-central generalized Gaussian distributions and we state some important properties related to the moments of this mixture. We estimate the distribution parameters using the expectation-maximization algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and kurtosis. The derived estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. We compare different predictive models and determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction.