Statistical Detection of EEG Synchrony Using Empirical Bayesian Inference

Abstract

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

An Implementation of Empirical Bayesian Inference and Non-Null Bootstrapping for Threshold Selection and Power Estimation in Multiple and Single Statistical Testing

“…In applications such as fMRI, the need for improved statistical inference has been explicitly emphasised by highlighting the limitations with existing techniques that lead to high false discovery rates (Eklund, Nichols, & Knutsson, 2016). The existing attempts to improve the statistical inference in EEG connectivity analysis (Singh, Asoh, & Phillips, 2011;Singh et al, 2015), have yield only partial success to date. Here, we used simulations to compare the EBI reports against the real truth.…”

“…Empirical Bayesian Inference (EBI) has shown promise in large-scale between-group comparisons (Efron, 2004(Efron, , 2007b, especially in genomics (Efron et al, 2001) and to some extent in the applications of neuroelectric signal and connectivity analysis (Singh, Asoh, Takeda, and Phillips, 2015). In EBI, constant prior probabilities are estimated from the data in large-scale multi-variable inferences or hypothesis testing and these priors are subsequently used to find the posterior probabilities using the estimated probability density functions of the pooled test statistics and the null distribution.…”