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Traditional causal connectivity methods in task-based and resting-state functional magnetic resonance imaging (fMRI) face challenges in accurately capturing directed information flow due to their sensitivity to noise and inability to model…
It is commonly assumed that a specific testing occasion (task, design, procedure, etc.) provides insights that generalise beyond that occasion. This assumption is infrequently carefully tested in data. We develop a statistically principled…
A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…
Functional connectivity (FC) analysis of resting-state fMRI data provides a framework for characterizing brain networks and their association with participant-level covariates. Due to the high dimensionality of neuroimaging data, standard…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…
Much recent attention has been paid to quantifying anatomic and functional neuroimaging on the individual subject level. For optimal individual subject characterization, specific acquisition and analysis features need to be identified that…
To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…
Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation…
Randomized controlled trials (RCTs) are the accepted standard for treatment effect estimation but they can be infeasible due to ethical reasons and prohibitive costs. Single-arm trials, where all patients belong to the treatment group, can…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
Analytical workflows in functional magnetic resonance imaging are highly flexible with limited best practices as to how to choose a pipeline. While it has been shown that the use of different pipelines might lead to different results, there…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them…
Functional connectivity (FC) derived from functional magnetic resonance imaging (fMRI) data offers vital insights for understanding brain function and neurological and psychiatric disorders. Unsupervised clustering methods are desired to…
When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be…
Flexible cognition requires the ability to rapidly detect systematic functions of variables and guide future behavior based on predictions. The model described here proposes a potential framework for patterns of neural activity to detect…
Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…