Computational Statistics & Data Analysis

EEG experiments yield high-dimensional event-related potential (ERP) data in response to repeatedly presented stimuli throughout the experiment. Changes in the high-dimensional ERP signal throughout the duration of an experiment (longitudinally) is the main quantity of interest in learning paradigms, where they represent the learning dynamics. Typical analysis, which can be performed in the time or the frequency domain, average the ERP waveform across all trials, leading to the loss of the potentially valuable longitudinal information in the data...

A functional data approach is developed to jointly estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. In this approach, the unconstrained relative curvature curves instead of the monotone-constrained functions are directly modeled. Functional principal components are used to describe the major modes of variations of curves and allow borrowing strength across curves for improved estimation. A two-step approach and an integrated approach are considered for model fitting...

It is shown how to overcome a new missing data problem in survival analysis. Iterative nonparametric techniques are utilized and the missing data information is both estimated and used for further estimation in each iterative step. Theory is developed and a good finite sample performance is illustrated by simulations. The main motivation is an application to French data on the temporal development of the number of hospitalized Covid-19 patients.

Survival analysis that involves moderate/high dimensional covariates has become common. Most of the existing analyses have been focused on estimation and variable selection, using penalization and other regularization techniques. To draw more definitive conclusions, a handful of studies have also conducted inference. The recently developed mFDR (marginal false discovery rate) technique provides an alternative inference perspective and can be advantageous in multiple aspects. The existing inference studies for regularized estimation of survival data with moderate/high dimensional covariates assume the Cox and other specific models, which may not be sufficiently flexible...

Generalized <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> -means can be combined with any similarity or dissimilarity measure for clustering. Using the well known likelihood ratio or <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> -statistic as the dissimilarity measure, a generalized <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> -means method is proposed to group generalized linear models (GLMs) for exponential family distributions...

In many rare disease Phase II clinical trials, two objectives are of interest to an investigator: maximising the statistical power and maximising the number of patients responding to the treatment. These two objectives are competing, therefore, clinical trial designs offering a balance between them are needed. Recently, it was argued that response-adaptive designs such as families of multi-arm bandit (MAB) methods could provide the means for achieving this balance. Furthermore, response-adaptive designs based on a concept of context-dependent (weighted) information criteria were recently proposed with a focus on Shannon's differential entropy...

The goal of the optimal treatment regime is maximizing treatment benefits via personalized treatment assignments based on the observed patient and treatment characteristics. Parametric regression-based outcome learning approaches require exploring complex interplay between the outcome and treatment assignments adjusting for the patient and treatment covariates, yet correctly specifying such relationships is challenging. Thus, a robust method against misspecified models is desirable in practice. Parsimonious models are also desired to pursue a concise interpretation and to avoid including spurious predictors of the outcome or treatment benefits...

A Bayesian approach is proposed that unifies Gaussian Bayesian network constructions and comparisons between two networks (identical or differential) for data with graph ordering unknown. When sampling graph ordering, to escape from local maximums, an adjusted single queue equi-energy algorithm is applied. The conditional posterior probability mass function for network differentiation is derived and its asymptotic proposition is theoretically assessed. Simulations are used to demonstrate the approach and compare with existing methods...

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open problem is how to estimate such models from large networks. A novel approach to large-scale estimation is proposed, taking advantage of the local structure of such models for the purpose of local computing. The main idea is that random graphs with local dependence can be decomposed into subgraphs, which enables parallel computing on subgraphs and suggests a two-step estimation approach...

Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression analysis. What has been less studied is the comparison of nonlinear functions. In lower-dimensional situations, inference typically involves comparisons of curves and surfaces. The existing comparative procedures are subject to various limitations, and few computational tools have been made available for off-the-shelf use. To address these limitations, two modified testing procedures for nonlinear curve and surface comparisons are proposed...

Biclustering is an important exploratory analysis tool that simultaneously clusters rows (e.g., samples) and columns (e.g., variables) of a data matrix. Checkerboard-like biclusters reveal intrinsic associations between rows and columns. However, most existing methods rely on Gaussian assumptions and only apply to matrix data. In practice, non-Gaussian and/or multi-way tensor data are frequently encountered. A new CO-clustering method via Regularized Alternating Least Squares (CORALS) is proposed, which generalizes biclustering to non-Gaussian data and multi-way tensor arrays...

The ordinal dominance curve (ODC) is a useful graphical tool to compare two population distributions. These distributions are said to satisfy uniform stochastic ordering (USO) if the ODC for them is star-shaped. A goodness-of-fit test for USO was recently proposed when both distributions are unknown. This test involves calculating the L p distance between an empirical estimator of the ODC and its least star-shaped majorant. The least favorable configuration of the two distributions was established so that proper critical values could be determined; i...

The finite mixture of regression (FMR) model is a popular tool for accommodating data heterogeneity. In the analysis of FMR models with high-dimensional covariates, it is necessary to conduct regularized estimation and identify important covariates rather than noises. In the literature, there has been a lack of attention paid to the differences among important covariates, which can lead to the underlying structure of covariate effects. Specifically, important covariates can be classified into two types: those that behave the same in different subpopulations and those that behave differently...

A novel borrowing strength measure and an overall borrowing index to characterize the strength of borrowing behaviors among subgroups are proposed for a given Bayesian hierarchical model. The constructions of the proposed indexes are based on the Mallow's distance and can be easily computed using MCMC samples for univariate or multivariate posterior distributions. Consequently, the proposed indexes can serve as meaningful and useful exploratory tools to better understand the roles played by the priors in a hierarchical model, including their influences on the posteriors that are used to make statistical inferences...

Field studies in ecology often make use of data collected in a hierarchical fashion, and may combine studies that vary in sampling design. For example, studies of tree recruitment after disturbance may use counts of individual seedlings from plots that vary in spatial arrangement and sampling density. To account for the multi-level design and the fact that more than a few plots usually yield no individuals, a mixed effects zero inflated Poisson model is often adopted. Although it is a convenient modeling strategy, various aspects of the model could be misspecified...

Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. When dealing with multiple mediators, which are potentially causally dependent, the possible decomposition of pathway effects grows exponentially with the number of mediators. An existing approach incorporated the principal component analysis (PCA) to address this challenge based on the fact that the transformed mediators are conditionally independent given the orthogonality of the principal components (PCs)...

Emerging brain connectivity network studies suggest that interactions between various distributed neuronal populations may be characterized by an organized complex topological structure. Many neuropsychiatric disorders are associated with altered topological patterns of brain connectivity. Therefore, a key inquiry of connectivity analysis is to detect group-level differentially expressed connectome patterns from the massive neuroimaging data. Recently, statistical methods have been developed to detect differentially expressed connectivity features at a subnetwork level, extending more commonly applied edge level analysis...

In a number of applications, one has access to high-dimensional time series data on several related subjects. A motivating application area comes from the neuroimaging field, such as brain fMRI time series data, obtained from various groups of subjects (cases/controls) with a specific neurological disorder. The problem of regularized joint estimation of multiple related Vector Autoregressive (VAR) models is discussed, leveraging a group lasso penalty in addition to a regular lasso one, so as to increase statistical efficiency of the estimates by borrowing strength across the models...

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions...

An optimal and flexible multiple hypotheses testing procedure is constructed for dependent data based on Bayesian techniques, aiming at handling two challenges, namely dependence structure and non-null distribution specification. Ignoring dependence among hypotheses tests may lead to loss of efficiency and bias in decision. Misspecification in the non-null distribution, on the other hand, can result in both false positive and false negative errors. Hidden Markov models are used to accommodate the dependence structure among the tests...