arXiv subjects

Thomas Maullin-Sapey

Publications and source records attributed to Thomas Maullin-Sapey.

3 recordsLinked to original sources

arXiv2026

False Discovery Controlled Regions for Excursion Sets

Identifying areas where the signal is prominent is an important task in image analysis, with particular applications in brain mapping. In this work, we develop False Discovery Controlled Regions (FDCRs) for excursion sets, the set of locations where the values are above or below a given level. We achieve this by treating the confidence procedure as a testing problem at the given level, allowing control of the False Discovery Rate (FDR). Methods are developed to control the FDR, separately for positive and negative excursions, as well as jointly over both. Furthermore, power is increased by incorporating a two-stage adaptive procedure. Simulation results in a variety of different settings show that the FDCRs successfully control the FDR under the nominal alpha level. We showcase our methods with an application to functional magnetic resonance imaging (fMRI) data from the Human Connectome Project illustrating the improvement in statistical power over existing approaches.

stat.ME↗

arXiv2022

Spatial Confidence Regions for Combinations of Excursion Sets in Image Analysis

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.

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arXiv2021

Fisher Scoring for crossed factor Linear Mixed Models

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.

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