The generalized shrinkage estimator for the analysis of functional connectivity of brain signals

We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may have poor frequency resolution. In this work, we develop the generalized shrinkage estimator, which is a weighted average of a parametric estimator and a nonparametric estimator. The optimal weights are frequency-specific and derived under the quadratic risk criterion so that the estimator, either the parametric estimator or the nonparametric estimator, that performs better at a particular frequency receives heavier weight. We validate the proposed estimator in a simulation study and apply it on electroencephalogram recordings from a visual-motor experiment.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS396 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian Model Search for Nonstationary Periodic Time Series

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo (MCMC) algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behaviour in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces.Comment: Received 23 Oct 2018, Accepted 12 May 201

Spectral analysis of high-dimensional time series

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length, regularisation based methods can overcome the curse of dimensionality, but the existing ones lack theoretical justification. This paper develops the first non-asymptotic result for characterising the difference between the sample and population versions of the spectral density matrix, allowing one to justify a range of high-dimensional models for analysing time series. As a concrete example, we apply this result to establish the convergence of the smoothed periodogram estimators and sparse estimators of the inverse of spectral density matrices, namely precision matrices. These results, novel in the frequency domain time series analysis, are corroborated by simulations and an analysis of the Google Flu Trends data

credsubs: Multiplicity-Adjusted Subset Identification

Subset identification methods are used to select the subset of a covariate space over which the conditional distribution of a response has certain properties - for example, identifying types of patients whose conditional treatment effect is positive. An often critical requirement of subset identification methods is multiplicity control, by which the family-wise Type I error rate is controlled, rather than the Type I error rate of each covariate-determined hypothesis separately. The credible subset (or credible subgroup) method provides a multiplicity-controlled estimate of the target subset in the form of two bounding subsets: one which entirely contains the target subset, and one which is entirely contained by it. We introduce a new R package, credsubs, which constructs credible subset estimates using a sample from the joint posterior distribution of any regression model, a description of the covariate space, and a function mapping the parameters and covariates to the subset criterion. We demonstrate parametric and nonparametric applications of the package to a clinical trial dataset and a neuroimaging dataset, respectively

Changes in sleep duration, quality, and medication use are prospectively associated with health and well-being : analysis of the UK Household Longitudinal Study

Introduction: Sleep is a plausible target for public health promotion. We examined the association of changes in sleep with subsequent health and well-being in the general population. Aims and Methods: We analyzed data from the UK Household Longitudinal Survey, involving 30594 people (aged > 16) who provided data on sleep and health and well-being at both Wave 1 (2009–2011) and Wave 4 (2012–2014) assessments. Predicting variables were changes in sleep quantity, sleep quality, and sleep medication use over the 4-year period. Outcome variables were the General Health Questionnaire (GHQ-12) and the 12-Item Short-Form Health Survey (SF-12) mental (MCS) and physical (PCS) component scores at Wave 4. Linear regression on each outcome was fully adjusted for potential confounders and baseline values of the relevant predicting and outcome variables. Results: Better outcomes were associated with an increase in sleep duration (GHQ: β = 1.031 [95% confidence interval {CI}: −1.328, −0.734]; MCS: 1.531 [1.006, 2.055]; PCS: −0.071 [−0.419, 0.56]), sleep quality (GHQ: β = −2.031 [95% CI: −2.218, −1.844]; MCS: 3.027 [2.692, 3.361]; PCS: 0.924 [0.604, 1.245]), and a reduction in sleep medication use (GHQ: β = −1.929 [95% CI: −2.400, −1.459]; MCS: 3.106 [2.279, 3.933]; PCS: 2.633 [1.860, 3.406]). Poorer outcomes were on the other hand associated with a reduction in sleep duration, a decrease in sleep quality, and an increase in sleep medication use. Changes in sleep quality yielded the largest effects on the health and well-being outcomes. Conclusions: Changes in sleep were temporally associated with subsequent health and well-being. Initiatives that aim to protect a critical amount of sleep, promote sleep quality, and reduce sleep medication use may have public health values

Identifying the recurrence of sleep apnea using a harmonic hidden Markov model

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces

Modeling the evolution of dynamic brain processes during an associative learning experiment

We develop a new time series model to investigate the dynamic interactions between the nucleus accumbens and the hippocampus during an associative learning experiment. Preliminary analyses indicated that the spectral properties of the local field potentials at these two regions changed over the trials of the experiment. While many models already take into account nonstationarity within a single trial, the evolution of the dynamics across trials is often ignored. Our proposed model, the slowly evolving locally stationary process (SEv-LSP), is designed to capture nonstationarity both within a trial and across trials. We rigorously define the evolving evolutionary spectral density matrix, which we estimate using a two-stage procedure. In the first stage, we compute the within-trial time-localized periodogram matrix. In the second stage, we develop a data-driven approach that combines information from trial-specific local periodogram matrices. Through simulation studies, we show the utility of our proposed method for analyzing time series data with different evolutionary structures. Finally, we use the SEv-LSP model to demonstrate the evolving dynamics between the hippocampus and the nucleus accumbens during an associative learning experiment