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Tensor-based morphometry (TBM) aims at showing local differences in brain volumes with respect to a common template. TBM images are smooth but they exhibit (especially in diseased groups) higher values in some brain regions called lateral ventricles. More specifically, our voxelwise analysis shows both a mean-variance relationship in these areas and evidence of spatially dependent skewness. We propose a model for 3-dimensional functional data where mean, variance, and skewness functions vary smoothly across brain locations. We model the voxelwise distributions as skew-normal. The smooth effects of age and sex are estimated on a reference population of cognitively normal subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and mapped across the whole brain. The three parameter functions allow to transform each TBM image (in the reference population as well as in a test set) into a Gaussian process. These subject-specific normative maps are used to derive indices of deviation from a healthy condition to assess the individual risk of pathological degeneration.

Bayesian Image-on-Scalar Regression (ISR) offers significant advantages for neuroimaging data analysis, including flexibility and the ability to quantify uncertainty. However, its application to large-scale imaging datasets, such as found in the UK Biobank, is hindered by the computational demands of traditional posterior computation methods, as well as the challenge of individual-specific brain masks that deviate from the common mask typically used in standard ISR approaches. To address these challenges, we introduce a novel Bayesian ISR model that is scalable and accommodates inconsistent brain masks across subjects in large-scale imaging studies. Our model leverages Gaussian process priors and integrates salience area indicators to facilitate ISR. We develop a cutting-edge scalable posterior computation algorithm that employs stochastic gradient Langevin dynamics coupled with memory mapping techniques, ensuring that computation time scales linearly with subsample size and memory usage is constrained only by the batch size. Our approach uniquely enables direct spatial posterior inferences on brain activation regions. The efficacy of our method is demonstrated through simulations and analysis of the UK Biobank task fMRI data, encompassing 38,639 subjects and over 120,000 voxels per image, showing that it can achieve a speed increase of 4 to 11 times and enhance statistical power by 8% to 18% compared to traditional Gibbs sampling with zero-imputation in various simulation scenarios.

In addressing the challenge of analysing the large-scale Adolescent Brain Cognition Development (ABCD) fMRI dataset, involving over 5,000 subjects and extensive neuroimaging data, we propose a scalable Bayesian scalar-on-image regression model for computational feasibility and efficiency. Our model employs a relaxed-thresholded Gaussian process (RTGP), integrating piecewise-smooth, sparse, and continuous functions capable of both hard- and soft-thresholding. This approach introduces additional flexibility in feature selection in scalar-on-image regression and leads to scalable posterior computation by adopting a variational approximation and utilising the Karhunen-Lo\`eve expansion for Gaussian processes. This advancement substantially reduces the computational costs in vertex-wise analysis of cortical surface data in large-scale Bayesian spatial models. The model's parameter estimation and prediction accuracy and feature selection performance are validated through extensive simulation studies and an application to the ABCD study. Here, we perform regression analysis correlating intelligence scores with task-based functional MRI data, taking into account confounding factors including age, sex, and parental education level. This validation highlights our model's capability to handle large-scale neuroimaging data while maintaining computational feasibility and accuracy., Comment: For supplementary materials, see https://drive.google.com/file/d/1SNS0T6ptIGLfs67zYrZ9Bz0-DgzCIRgz/view?usp=sharing . For code, see https://github.com/annamenacher/RTGP

False discovery rate (FDR) is commonly used for correction for multiple testing in neuroimaging studies. However, when using two-tailed tests, making directional inferences about the results can lead to vastly inflated error rate, even approaching 100\% in some cases. This happens because FDR only provides weak control over the error rate, meaning that the proportion of error is guaranteed only globally over all tests, not within subsets, such as among those in only one or another direction. Here we consider and evaluate different strategies for FDR control with two-tailed tests, using both synthetic and real imaging data. Approaches that separate the tests by direction of the hypothesis test, or by the direction of the resulting test statistic, more properly control the directional error rate and preserve FDR benefits, albeit with a doubled risk of errors under complete absence of signal. Strategies that combine tests in both directions, or that use simple two-tailed p-values, can lead to invalid directional conclusions, even if these tests remain globally valid. To enable valid thresholding for directional inference, we suggest that imaging software should allow the possibility that the user sets asymmetrical thresholds for the two sides of the statistical map. While FDR continues to be a valid, powerful procedure for multiple testing correction, care is needed when making directional inferences for two-tailed tests, or more broadly, when making any localized inference., Comment: 27 pages, 3 figures, 2 tables, 39 references

Historically, applications of RFT in fMRI have relied on assumptions of smoothness, stationarity and Gaussianity. The first two assumptions have been addressed in Part 1 of this article series. Here we address the severe non-Gaussianity of (real) fMRI data to greatly improve the performance of voxelwise RFT in fMRI group analysis. In particular, we introduce a transformation which accelerates the convergence of the Central Limit Theorem allowing us to rely on limiting Gaussianity of the test-statistic. We shall show that, when the GKF is combined with the Gaussianization transformation, we are able to accurately estimate the EEC of the excursion set of the transformed test-statistic even when the data is non-Gaussian. This allows us to drop the key assumptions of RFT inference and enables us to provide a fast approach which correctly controls the voxelwise false positive rate in fMRI. We employ a big data \cite{Eklund2016} style validation in which we process resting state data from 7000 subjects from the UK BioBank with fake task designs. We resample from this data to create realistic noise and use this to demonstrate that the error rate is correctly controlled.

The Brain Imaging Data Structure (BIDS) is a community-driven standard for the organization of data and metadata from a growing range of neuroscience modalities. This paper is meant as a history of how the standard has developed and grown over time. We outline the principles behind the project, the mechanisms by which it has been extended, and some of the challenges being addressed as it evolves. We also discuss the lessons learned through the project, with the aim of enabling researchers in other domains to learn from the success of BIDS.

Coordinate-based meta-analysis combines evidence from a collection of Neuroimaging studies to estimate brain activation. In such analyses, a key practical challenge is to find a computationally efficient approach with good statistical interpretability to model the locations of activation foci. In this article, we propose a generative coordinate-based meta-regression (CBMR) framework to approximate smooth activation intensity function and investigate the effect of study-level covariates (e.g., year of publication, sample size). We employ spline parameterization to model spatial structure of brain activation and consider four stochastic models for modelling the random variation in foci. To examine the validity of CBMR, we estimate brain activation on $20$ meta-analytic datasets, conduct spatial homogeneity tests at voxel level, and compare to results generated by existing kernel-based approaches.

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions., Comment: 19 pages, 1 figure, 1 box

Cluster inference based on spatial extent thresholding is the most popular analysis method for finding activated brain areas in neuroimaging. However, the method has several well-known issues. While powerful for finding brain regions with some activation, the method as currently defined does not allow any further quantification or localization of signal. In this paper we repair this gap. We show that cluster-extent inference can be used (1.) to infer the presence of signal in anatomical regions of interest and (2.) to quantify the percentage of active voxels in any cluster or region of interest. These additional inferences come for free, i.e. they do not require any further adjustment of the alpha-level of tests, while retaining full familywise error control. We achieve this extension of the possibilities of cluster inference by an embedding of the method into a closed testing procedure, and solving the graph-theoretic k-separator problem that results from this embedding. The new method can be used in combination with random field theory or permutations. We demonstrate the usefulness of the method in a large-scale application to neuroimaging data from the Neurovault database.

Local maxima of random processes are useful for finding important regions and are routinely used, for summarising features of interest (e.g. in neuroimaging). In this work we provide confidence regions for the location of local maxima of the mean and standardized effect size (i.e. Cohen's d) given multiple realisations of a random process. We prove central limit theorems for the location of the maximum of mean and t-statistic random fields and use these to provide asymptotic confidence regions for the location of peaks of the mean and Cohen's d. Under the assumption of stationarity we develop Monte Carlo confidence regions for the location of peaks of the mean that have better finite sample coverage than regions derived based on classical asymptotic normality. We illustrate our methods on 1D MEG data and 2D fMRI data from the UK Biobank.

Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture priors on spatially-varying parameters and enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimization, allows our method to scale to large sample sizes. Our method also accounts for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach based on Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Lastly, we validate our results via simulation studies and an application to the UK Biobank, a large-scale lesion mapping study with a sample size of 40,000 subjects., Comment: For supplementary materials, see https://drive.google.com/file/d/1vr154MEsxv00OMeZQR8R4ecpd5V35qCa/view?usp=sharing . For code, see https://github.com/annamenacher/BLESS ${.}$

The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology and cosmology. Despite growing literature, there is little published concerning the comparison of processes that have been sampled across the same spatial region but which reflect different study conditions. Given a set of asymptotically Gaussian random fields, each corresponding to a sample acquired for a different study condition, this work aims to provide confidence statements about the intersection, or union, of the excursion sets across all fields. Such spatial regions are of natural interest as they directly correspond to the questions "all random fields exceed a predetermined threshold?", or "Where does at least one random field exceed a predetermined threshold?". To assess the degree of spatial variability present, we develop a method that provides, with a desired confidence, subsets and supersets of spatial regions defined by logical conjunctions (i.e. set intersections) or disjunctions (i.e. set unions), without any assumption on the dependence between the different fields. The method is verified by extensive simulations and demonstrated using a task-fMRI dataset to identify brain regions with activation common to four variants of a working memory task., Comment: For Supplementary Theory see https://drive.google.com/file/d/1hXhrstxlHY_MMjfwE3VxPQYxp0N6JMp2/view?usp=sharing . For Supplementary Results see https://drive.google.com/file/d/156EUIYq1YIJblXI4etYmT1JRjdVpQNhf/view?usp=sharing . For code see https://github.com/TomMaullin/ConfSets

The analysis of longitudinal, heterogeneous or unbalanced clustered data is of primary importance to a wide range of applications. The Linear Mixed Model (LMM) is a popular and flexible extension of the linear model specifically designed for such purposes. Historically, a large proportion of material published on the LMM concerns the application of popular numerical optimization algorithms, such as Newton-Raphson, Fisher Scoring and Expectation Maximization to single-factor LMMs (i.e. LMMs that only contain one "factor" by which observations are grouped). However, in recent years, the focus of the LMM literature has moved towards the development of estimation and inference methods for more complex, multi-factored designs. In this paper, we present and derive new expressions for the extension of an algorithm classically used for single-factor LMM parameter estimation, Fisher Scoring, to multiple, crossed-factor designs. Through simulation and real data examples, we compare five variants of the Fisher Scoring algorithm with one another, as well as against a baseline established by the R package lmer, and find evidence of correctness and strong computational efficiency for four of the five proposed approaches. Additionally, we provide a new method for LMM Satterthwaite degrees of freedom estimation based on analytical results, which does not require iterative gradient estimation. Via simulation, we find that this approach produces estimates with both lower bias and lower variance than the existing methods., Comment: For supplementary material see https://www.overleaf.com/read/bvscgqrvqnjh . For code and notebooks, see https://github.com/TomMaullin/LMMPaper

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA., Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 references

One-sided t-tests are commonly used in the neuroimaging field, but two-sided tests should be the default unless a researcher has a strong reason for using a one-sided test. Here we extend our previous work on cluster false positive rates, which used one-sided tests, to two-sided tests. Briefly, we found that parametric methods perform worse for two-sided t-tests, and that non-parametric methods perform equally well for one-sided and two-sided tests.

Methodological research rarely generates a broad interest, yet our work on the validity of cluster inference methods for functional magnetic resonance imaging (fMRI) created intense discussion on both the minutia of our approach and its implications for the discipline. In the present work, we take on various critiques of our work and further explore the limitations of our original work. We address issues about the particular event-related designs we used, considering multiple event types and randomisation of events between subjects. We consider the lack of validity found with one-sample permutation (sign flipping) tests, investigating a number of approaches to improve the false positive control of this widely used procedure. We found that the combination of a two-sided test and cleaning the data using ICA FIX resulted in nominal false positive rates for all datasets, meaning that data cleaning is not only important for resting state fMRI, but also for task fMRI. Finally, we discuss the implications of our work on the fMRI literature as a whole, estimating that at least 10% of the fMRI studies have used the most problematic cluster inference method (P = 0.01 cluster defining threshold), and how individual studies can be interpreted in light of our findings. These additional results underscore our original conclusions, on the importance of data sharing and thorough evaluation of statistical methods on realistic null data.

By constructing a sampling distribution for DVARS we can create a standardized version of DVARS that should be more similar across scanners and datasets., Comment: 5 pages

Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected $p$-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing procedure as the construction of a very large permutation testing matrix, $T$, one can exploit structural properties derived from the data and the test statistics to reduce the runtime under certain conditions. In particular, we see that $T$ is low-rank plus a low-variance residual. This makes $T$ a good candidate for low-rank matrix completion, where only a very small number of entries of $T$ ($\sim0.35\%$ of all entries in our experiments) have to be computed to obtain a good estimate. Based on this observation, we present RapidPT, an algorithm that efficiently recovers the max null distribution commonly obtained through regular permutation testing in voxel-wise analysis. We present an extensive validation on a synthetic dataset and four varying sized datasets against two baselines: Statistical NonParametric Mapping (SnPM13) and a standard permutation testing implementation (referred as NaivePT). We find that RapidPT achieves its best runtime performance on medium sized datasets ($50 \leq n \leq 200$), with speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger datasets ($n \geq 200$) RapidPT outperforms NaivePT (6x - 200x) on all datasets, and provides large speedups over SnPM13 when more than 10000 permutations (2x - 15x) are needed. The implementation is a standalone toolbox and also integrated within SnPM13, able to leverage multi-core architectures when available., Comment: 36 pages, 16 figures

A recent Editorial by Slotnick (2017) reconsiders the findings of our paper on the accuracy of false positive rate control with cluster inference in fMRI (Eklund et al, 2016), in particular criticising our use of resting state fMRI data as a source for null data in the evaluation of task fMRI methods. We defend this use of resting fMRI data, as while there is much structure in this data, we argue it is representative of task data noise and as such analysis software should be able to accommodate this noise. We also discuss a potential problem with Slotnick's own method., Comment: Update: Title changed to be more informative, abstract expanded. Body text unchanged

Working memory (WM) was one of the first cognitive processes studied with functional magnetic resonance imaging. With now over 20 years of studies on WM, each study with tiny sample sizes, there is a need for meta-analysis to identify the brain regions that are consistently activated by WM tasks, and to understand the interstudy variation in those activations. However, current methods in the field cannot fully account for the spatial nature of neuroimaging meta-analysis data or the heterogeneity observed among WM studies. In this work, we propose a fully Bayesian random-effects metaregression model based on log-Gaussian Cox processes, which can be used for meta-analysis of neuroimaging studies. An efficient Markov chain Monte Carlo scheme for posterior simulations is presented which makes use of some recent advances in parallel computing using graphics processing units. Application of the proposed model to a real data set provides valuable insights regarding the function of the WM.