Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Munk, Axel Prof. Dr."
Now showing items 1-20 of 31
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Statistical Optimal Transport and its Entropic Regularization: Compared and Contrasted
(2024-04-26)In recent years, statistical methodology based on optimal transport witnessed a considerable increase in practical and theoretical interest. A central reason for this trend is the ability of optimal transport to compare ... -
Statistical and Structural Aspects of Unbalanced Optimal Transport Barycenters
(2022-10-20)Optimal transport (OT) has seen a stellar rise in interest and relevance in the past two decades. More recently, severe limitation of OT have started to surface. Two key factors prevent it from becoming a standard tool in ... -
Contributions to the Theory of Statistical Optimal Transport
(2022-07-01)The application of optimal transport based methodologies for statistical purposes has experienced a surge of interest and activity in recent years. This doctoral thesis collects the work of four research articles on the ... -
On minimax detection of localized signals from indirect or correlated data
(2022-05-05)This is a cumulative thesis consisting of two papers, in which we treat two problems related to the detectability of local anomalies within certain types of data. In the first paper, we suppose that a segment of a Gaussian ... -
Limit Laws for Empirical Optimal Transport
(2022-02-17)Optimal Transport (OT) has recently gained increasing attention in various fields ranging from biology to machine learning and mathematics. Especially OT based dissimilarity measures can be designed to respect the underlying ... -
A Statistical Model of Microscope Resolution
(2020-07-10)A general rule of thumb in imaging is that the resolution of a light microscope depends linearly on the full width at half maximum (FWHM) of its point spread function (psf). In the present work we carefully define a ... -
Multiscale Total Variation Estimators for Regression and Inverse Problems
(2019-06-28)In the context of nonparametric regression and inverse problems, variational multiscale methods combine multiscale dictionaries with regularization functionals in a variational framework. In recent years, these methods ... -
Semiparametric Estimation of Drift, Rotation and Scaling in Sparse Sequential Dynamic Imaging: Asymptotic theory and an application in nanoscale fluorescence microscopy
(2019-02-28)Light microscopy is an important instrument in life sciences. Over the last two decades, superresolution fluorescence microscopy techniques have been established, breaking the Abbé diffraction barrier, which before had ... -
Empirical Optimal Transport on Discrete Spaces: Limit Theorems, Distributional Bounds and Applications
(2019-01-09)Optimal Transport and especially distances based on optimal transport are a widely applied tool in different mathematical disciplines. Among others it is used in probability theory to study for example limit laws or derive ... -
Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings
(2018-02-09)Ion channel recordings by the patch clamp technique are a major tool to quantify the electrophysiological dynamics of ion channels in the cell membrane, which is for instance important in medicine for the development of ... -
Finite Alphabet Blind Separation
(2018-01-04)This thesis considers a particular blind source separation problem, where the sources are assumed to only take values in a known finite set, denoted as the alphabet. More precisely, one observes M linear mixtures of m ... -
Inference in inhomogeneous hidden Markov models with application to ion channel data
(2017-12-18)Ion channel recordings under a changing environment are hardly analyzed and are the main cause for the new model class we introduce. This thesis mainly concerns hidden Markov models with a homogeneous hidden Markov chain ... -
Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms
(2017-12-07)Wasserstein distances or, more generally, distances that quantify the optimal transport between probability measures on metric spaces have long been established as an important tool in probability theory. More recently, ... -
Estimating rigid motion in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy
(2017-04-05)In this work, we deal with sequences of pixel images (frames) which are noisy shifted, rotated, and scaled versions of some unknown image f. Moreover, those frames are sparse in the sense that they do not show the whole ... -
Multiscale Change-point Segmentation: Beyond Step Functions
(2017-03-08)Many multiscale segmentation methods have been proven to work successfully for detecting multiple change-points, mainly because they provide faithful statistical statements, while at the same time allowing for efficient ... -
Variational Estimators in Statistical Multiscale Analysis
(2016-05-24)In recent years, a novel type of multiscale variational statistical approaches, based on so-called multiscale statistics, have received increasing popularity in various applications, such as signal recovery, imaging and ... -
Fourier and Variational Based Approaches for Fingerprint Segmentation
(2015-05-22)Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing ... -
Simultaneous Confidence Statements about the Diffusion Coefficient of an Ito-Process with Application to Spot Volatility Estimation
(2014-07-28)In this PhD thesis, we address the problem of giving simultaneous confidence statements about local features of the diffusion of an Itô process. To this end, we construct a multiscale test based on weighted quadratic ... -
Statistical Multiscale Segmentation: Inference, Algorithms and Applications
(2014-03-31)This thesis mainly concerns change-point models with independent observations from an exponential family with constant mean in between change-points. An inferential scheme for estimation and confidence statements based ... -
Ein semiparametrisches Verfahren zur Planung und Auswertung von Nichtunterlegenheitsstudien im Cox-Modell
(2012-03-06)In this dissertation we develop a statistical method for planning and evaluating non-inferiority trials for right censored time to event data in the gold standard design. In clinical trials ...