We model the Alzheimer\'s Disease-related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies as sparse functional data and propose nonparametric test procedures to detect functional genotype effects while controlling the confounding effects of environmental covariates. Our new functional analysis of covariance tests are based on a seemingly unrelated kernel smoother, which takes into account the within-subject temporal correlations, and thus enjoy improved power over existing functional tests. We show that the proposed test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. Data used in the preparation of this article were obtained from the Alzheimer\'s Disease Neuroimaging Initiative (ADNI) database, where an application of the proposed test lead to the discovery of new genes that may be related to Alzheimer\'s Disease.

The field of neurotrauma is grappling with the effects of the recently identified replication crisis. As such, care must be taken to identify and perform the most appropriate statistical analyses. This will prevent misuse of research resources and ensure that conclusions are reasonable and within the scope of the data. We anticipate that Bayesian statistical methods will see increasing use in the coming years. Bayesian methods integrate prior beliefs (or prior data) into a statistical model to merge historical information and current experimental data. These methods may improve the ability to detect differences between experimental groups (i.e., statistical power) when used appropriately. However, researchers need to be aware of the strengths and limitations of such approaches if they are to implement or evaluate these analyses. Ultimately, an approach using Bayesian methodologies may have substantial benefits to statistical power, but caution needs to be taken when identifying and defining prior beliefs.

A central challenge in hypothesis testing (HT) lies in determining the optimal balance between Type I (false positive) and Type II (non-detection or false negative) error probabilities. Analyzing these errors\' exponential rate of convergence, known as error exponents, provides crucial insights into system performance. Error exponents offer a lens through which we can understand how operational restrictions, such as resource constraints and impairments in communications, affect the accuracy of distributed inference in networked systems. This survey presents a comprehensive review of key results in HT, from the foundational Stein\'s Lemma to recent advancements in distributed HT, all unified through the framework of error exponents. We explore asymptotic and non-asymptotic results, highlighting their implications for designing robust and efficient networked systems, such as event detection through lossy wireless sensor monitoring networks, collective perception-based object detection in vehicular environments, and clock synchronization in distributed environments, among others. We show that understanding the role of error exponents provides a valuable tool for optimizing decision-making and improving the reliability of networked systems.

From an early age, children explore their environment in a way suggesting that they reason about causal variables and seek causal explanations. Indeed, following extensive studies of problem-solving abilities in chimpanzees, Povinelli (Folk Physics for Apes, Oxford University Press, 2000) proposed that this ability to reason about unobservable variables is unique to humans. Following on from this, Povinelli and Dunphy-Lelii (Canadian Journal of Experimental Psychology, 55(2), 187-195, 2001) addressed the question whether chimpanzees would explore objects with the aim of elucidating unobservable and surprising object properties. Chimpanzees, unlike preschool children, did not show increased object exploration following a change in the unobservable properties of an object. We critically discuss these findings and argue that more research using a greater variety of methods and with a larger number of species is required to support the hypothesis that only humans engage in explanation seeking. We conclude by highlighting avenues for future research based on developmental and comparative research aimed at object exploration and information seeking conducted since the original investigation by Povinelli and Dunphy-Lelii.

Within-individual coupling between measures of brain structure and function evolves in development and may underlie differential risk for neuropsychiatric disorders. Despite increasing interest in the development of structure-function relationships, rigorous methods to quantify and test individual differences in coupling remain nascent. In this article, we explore and address gaps in approaches for testing and spatially localizing individual differences in intermodal coupling. We propose a new method, called CIDeR, which is designed to simultaneously perform hypothesis testing in a way that limits false positive results and improve detection of true positive results. Through a comparison across different approaches to testing individual differences in intermodal coupling, we delineate subtle differences in the hypotheses they test, which may ultimately lead researchers to arrive at different results. Finally, we illustrate the utility of CIDeR in two applications to brain development using data from the Philadelphia Neurodevelopmental Cohort.

Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

Functional networks often guide our interpretation of spatial maps of brain-phenotype associations. However, methods for assessing enrichment of associations within networks of interest have varied in terms of both scientific rigor and underlying assumptions. While some approaches have relied on subjective interpretations, others have made unrealistic assumptions about spatial properties of imaging data, leading to inflated false positive rates. We seek to address this gap in existing methodology by borrowing insight from a method widely used in genetics research for testing enrichment of associations between a set of genes and a phenotype of interest. We propose network enrichment significance testing (NEST), a flexible framework for testing the specificity of brain-phenotype associations to functional networks or other sub-regions of the brain. We apply NEST to study enrichment of associations with structural and functional brain imaging data from a large-scale neurodevelopmental cohort study.

This article considers a way to test the hypothesis that two collections of objects are from the same uniform distribution of such objects. The exact p-value is calculated based on the distribution for the observed overlaps. In addition, an interval estimate of the number of distinct objects, when all objects are equally likely, is indicated.

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Classical tests for a difference in means control the type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated type I error rate. Notably, this problem persists even if two separate and independent data sets are used to define the groups and to test for a difference in their means. To address this problem, in this paper, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective type I error rate by accounting for the fact that the choice of null hypothesis was made based on the data. We describe how to efficiently compute exact p-values for clusters obtained using agglomerative hierarchical clustering with many commonly-used linkages. We apply our method to simulated data and to single-cell RNA-sequencing data.