Bayesian tapering test for comparing two spectral densities with application to EEG data

Human brain is still a mystery and finding the possible relationships between different parts of the brain is an important and unsolved topic. Our research provides a new perspective to explore this mystery by looking at the stereotactic electroencephalography (SEEG) data recorded when the subject is performing the gambling task. Motivated by this SEEG dataset, a novel tapering test is proposed for comparing the spectral density of two independent stationary time series. The key of proposed test is the form of test statistic as the tapered sum of squared summary coefficients, which are defined based on kernel-smoothed log-periodograms as estimates for log-spectrum. Furthermore, when replication exists, the corresponding tapering testing procedures are investigated. The asymptotic performance of proposed tests is evaluated through the “rate of testing” theory, a framework to find the rate at which the power is retained under geometric smoothness constraints. Driven by the practical needs, Bayesian tapering test and Bayesian multiple testing procedures are explored. Additionally, the empirical advantage of the proposed tapering test is demonstrated through a comprehensive simulation study. And the motivating SEEG data, collected from probes inserted into the skull of human subject, serves as the illustration of the approach developed here.