Dr. rer. nat. Fabian Joachim Erich Telschow

Profil

Zusammenfassung

Dr. Telschow entwickelt statistische Methoden zur Quantifizierung von Unsicherheiten in hochdimensionalen Daten, insbesondere für die Neuroimaging-Analyse. Seine Expertise liegt in der Konstruktion von Konfidenzintervallen und -bändern für funktionale Daten sowie in der robusten statistischen Inferenz bei räumlichen Daten. Diese Methoden adressieren praktische Probleme wie die Vermeidung von Fehlinterpretationen bei großen Stichproben und die präzise Lokalisierung von Effekten in Gehirnbildern.

Skills

Name

Dr. rer. nat. Fabian Joachim Erich Telschow

Titel

Dr. rer. nat.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Angewandte Mathematik

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Zuletzt gescrapt

28.6.2026, 01:13:36

• EXC 2046/1: MATH+ Junior Research Group on Statistical Inversion and Quantification of Uncertainties

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  Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 09/2020 - 12/2025 Projektleitung: Dr. rer. nat. Fabian Joachim Erich Telschow

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• Confidence Sets for Cohen’s d effect size images

  2020

  NeuroImage · 59 Zitationen · DOI

  Current statistical inference methods for task-fMRI suffer from two fundamental limitations. First, the focus is solely on detection of non-zero signal or signal change, a problem that is exacerbated for large scale studies (e.g. UK Biobank, N=40,000+) where the 'null hypothesis fallacy' causes even trivial effects to be determined as significant. Second, for any sample size, widely used cluster inference methods only indicate regions where a null hypothesis can be rejected, without providing any notion of spatial uncertainty about the activation. In this work, we address these issues by developing spatial Confidence Sets (CSs) on clusters found in thresholded Cohen's d effect size images. We produce an upper and lower CS to make confidence statements about brain regions where Cohen's d effect sizes have exceeded and fallen short of a non-zero threshold, respectively. The CSs convey information about the magnitude and reliability of effect sizes that is usually given separately in a t-statistic and effect estimate map. We expand the theory developed in our previous work on CSs for %BOLD change effect maps (Bowring et al., 2019) using recent results from the bootstrapping literature. By assessing the empirical coverage with 2D and 3D Monte Carlo simulations resembling fMRI data, we find our method is accurate in sample sizes as low as N=60. We compute Cohen's d CSs for the Human Connectome Project working memory task-fMRI data, illustrating the brain regions with a reliable Cohen's d response for a given threshold. By comparing the CSs with results obtained from a traditional statistical voxelwise inference, we highlight the improvement in activation localization that can be gained with the Confidence Sets.

• Spatial confidence sets for raw effect size images

  2019

  NeuroImage · 26 Zitationen · DOI

  The mass-univariate approach for functional magnetic resonance imaging (fMRI) analysis remains a widely used statistical tool within neuroimaging. However, this method suffers from at least two fundamental limitations: First, with sufficient sample sizes there is high enough statistical power to reject the null hypothesis everywhere, making it difficult if not impossible to localize effects of interest. Second, with any sample size, when cluster-size inference is used a significant p-value only indicates that a cluster is larger than chance. Therefore, no notion of confidence is available to express the size or location of a cluster that could be expected with repeated sampling from the population. In this work, we address these issues by extending on a method proposed by Sommerfeld et al. (2018) (SSS) to develop spatial Confidence Sets (CSs) on clusters found in thresholded raw effect size maps. While hypothesis testing indicates where the null, i.e. a raw effect size of zero, can be rejected, the CSs give statements on the locations where raw effect sizes exceed, and fall short of, a non-zero threshold, providing both an upper and lower CS. While the method can be applied to any mass-univariate general linear model, we motivate the method in the context of blood-oxygen-level-dependent (BOLD) fMRI contrast maps for inference on percentage BOLD change raw effects. We propose several theoretical and practical implementation advancements to the original method formulated in SSS, delivering a procedure with superior performance in sample sizes as low as N=60. We validate the method with 3D Monte Carlo simulations that resemble fMRI data. Finally, we compute CSs for the Human Connectome Project working memory task contrast images, illustrating the brain regions that show a reliable %BOLD change for a given %BOLD threshold.

• Simultaneous Confidence Bands for Functional Data Using the Gaussian Kinematic Formula

  2019

  arXiv (Cornell University) · 23 Zitationen · DOI

  This article constructs simultaneous confidence bands (SCBs) for functional parameters using the Gaussian Kinematic formula of $t$-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the parameter of interest is enough to obtain asymptotically precise covering rates even for non-Gaussian processes. As a proof of concept we study the functional signal-plus-noise model and derive a CLT for an estimator of the Lipschitz-Killing curvatures, the only data dependent quantities in the tGKF SCBs. Extensions to discrete sampling with additive observation noise are discussed using scale space ideas from regression analysis. Here we provide sufficient conditions on the processes and kernels to obtain convergence of the functional scale space surface. The theoretical work is accompanied by a simulation study comparing different methods to construct SCBs for the population mean. We show that the tGKF works well even for small sample sizes and only a Rademacher multiplier-$t$ bootstrap performs similarily well. For larger sample sizes the tGKF often outperforms the bootstrap methods and is computational faster. We apply the method to diffusion tensor imaging (DTI) fibers using a scale space approach for the difference of population means. R code is available in our Rpackage SCBfda.

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