Naveen N. Narisetty

Bayesian variable selection with shrinking and diffusing priors

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the

Extremal Depth for Functional Data and Applications

L_0

Investigating a Novel Measure of Brain Networking Following Sports Concussion

penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives.

Stability of an ERP-based measure of brain network activation (BNA) in athletes: A new electrophysiological assessment tool for concussion

ABSTRACT We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous coverage probability; (b) there is a correspondence between ED-based (simultaneous) central regions and appropriate pointwise central regions; and (c) the method is resistant to certain classes of functional outliers. The article examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. Supplementary materials for this article are available online.

Bayesian Regularization for Graphical Models with Unequal Shrinkage

Clinicians managing sports-related concussions are left to their clinical judgment in making diagnoses and return-to-play decisions. This study was designed to evaluate the utility of a novel measure of functional brain networking for concussion management. 24 athletes with acutely diagnosed concussion and 21 control participants were evaluated in a research laboratory. At each of the 4 post-injury time points, participants completed the Axon assessment of neurocognitive function, a self-report symptom inventory, and the auditory oddball and go/no-go tasks while electroencephalogram (EEG) readings were recorded. Brain Network Activation (BNA) scores were calculated from EEG data related to the auditory oddball and go/no-go tasks. BNA scores were unable to differentiate between the concussed and control groups or by self-report symptom severity. These findings conflict with previous work implementing electrophysiological assessments in concussed athletes, suggesting that BNA requires additional investigation and refinement before clinical implementation.

A New Approach to Censored Quantile Regression Estimation

Abstract Primary objective: To determine test–re-test reliabilities of novel Evoked Response Potential (ERP)-based Brain Network Activation (BNA) scores in healthy athletes. Research design: Observational, repeated-measures study. Methods and design: Forty-two healthy male and female high school and collegiate athletes completed auditory oddball and go/no-go ERP assessments at baseline, 1 week, 6 weeks and 1 year. The BNA algorithm was applied to the ERP data, considering electrode location, frequency band, peak latency and normalized amplitude to generate seven unique BNA scores for each testing session. Main outcomes and results: Mean BNA scores, intra-class correlation coefficient (ICC) values and reliable change (RC) values were calculated for each of the seven BNA networks. BNA scores ranged from 46.3 ± 34.9 to 69.9 ± 22.8, ICC values ranged from 0.46–0.65 and 95% RC values ranged from 38.3–68.1 across the seven networks. Conclusions: The wide range of BNA scores observed in this population of healthy athletes suggests that a single BNA score or set of BNA scores from a single after-injury test session may be difficult to interpret in isolation without knowledge of the athlete’s own baseline BNA score(s) and/or the results of serial tests performed at additional time points. The stability of each BNA network should be considered when interpreting test–re-test BNA score changes.

Robust multivariate mixture regression models with incomplete data

ABSTRACT We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new nonconvex penalty approximating the ℓ0 penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. Through extensive simulation studies and a real application to a call center data, we have demonstrated the fine performance of our method compared with existing alternatives. Supplementary materials for this article are available online.

Discussion of “multivariate functional outlier detection”

ABSTRACT Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly censored data. In this article, we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data. Supplementary material for this article is available online.

Application of Multivariate Sensitivity Analysis Techniques to AGCM-Simulated Tropical Cyclones

ABSTRACT Multivariate mixture regression models can be used to investigate the relationships between two or more response variables and a set of predictor variables by taking into consideration unobserved population heterogeneity. It is common to take multivariate normal distributions as mixing components, but this mixing model is sensitive to heavy-tailed errors and outliers. Although normal mixture models can approximate any distribution in principle, the number of components needed to account for heavy-tailed distributions can be very large. Mixture regression models based on the multivariate t distributions can be considered as a robust alternative approach. Missing data are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this paper, we propose a multivariate t mixture regression model with missing information to model heterogeneity in regression function in the presence of outliers and missing values. Along with the robust parameter estimation, our proposed method can be used for (i) visualization of the partial correlation between response variables across latent classes and heterogeneous regressions, and (ii) outlier detection and robust clustering even under the presence of missing values. We also propose a multivariate t mixture regression model using MM-estimation with missing information that is robust to high-leverage outliers. The proposed methodologies are illustrated through simulation studies and real data analysis.

Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection

In our comments we provide two possible modifications of the “centrality-stability plot (CSP)” proposed by Hubert, Rousseeuw and Segaert, which may, in some cases, make the plot more informative in flagging functional outliers.