Cross frequency coupling (CFC) between electrophysiological signals in the brain has been observed and it's abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling do not attempt to capture the underlying statistical relationships that give rise to this coupling. In this paper, we demonstrate a new method of calculating phase amplitude coupling by estimating the mutual information between phase and amplitude, using a flexible parametric modeling approach. Specifically, we develop an exponential generalized linear model (GLM) to model amplitude given phase, using a high dimensional basis of von-Mises function regressors and l1 regularized model selection. Using synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase amplitude coupling through receiver operating characteristic (ROC) curve analysis.