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- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Hillen, Thomas (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Kashlak, Adam (Mathematical and Statistical Sciences)
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Advances in Distributional Reinforcement Learning: Bridging Theory with Algorithmic Practice
DownloadFall 2024
This thesis comprehensively investigates Distributional Reinforcement Learning~(RL), a vibrant research field that interplays between statistics and RL. As an extension of classical RL, distributional RL, on the one hand, embraces plenty of statistical ideas by incorporating distributional...
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Fall 2024
Let Cat(oo,oo) denote the (oo,1)-category of (oo,oo)-categories with weakly inductive equivalences. The main objective of this thesis is to demonstrate that Cat(oo,oo) satisfies universal properties with respect to homotopy-coherent internalisation and enrichment. To achieve these universal...
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Statistical Learning and Inference For Functional Predictor Models via Reproducing Kernel Hilbert Space
DownloadFall 2024
Functional regression is a cornerstone for understanding complex relationships where predictors or responses (or both) are functions. A particularly powerful framework within this domain is the Reproducing Kernel Hilbert Space (RKHS), which facilitates the handling of infinite-dimensional data...
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Fall 2024
We begin with a survey of mathematical epidemic modelling from its inception to present day. We present up-to-date research on the field of variable susceptibility SIR (Susceptible-Infected-Removed system of differential equations model), which takes the classic SIR model and adds another...
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Fall 2024
Motivated by Elizabeth Meckes’ work on concentration inequalities using the group SO(n) (see [9]), this thesis explores the use of random rotations for detecting autocorrelation in time series data. Traditional tests like the Durbin Watson test assess autocorrelation by analyzing quadratic forms...
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Fall 2024
The interplay between order structure and probability theory has long been studied. In recent years this has led a generalization of many of the concepts from probability theory to arbitrary vector lattices. In this thesis, we study the generalization of discrete stopping times in vector...
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Fall 2024
We study the Severi varieties of Atiyah ruled surfaces over generic elliptic curves. In particular, we prove that general members of such varieties have at worst ordinary triple points.
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Fall 2024
Increased anthropogenic greenhouse gas emissions have gained attention from researchers and world leaders due to the potential for global warming. Part of the primary greenhouse gas emitters come from the agriculture and oil and gas industrial sectors. The sources of two prioritized greenhouse...
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Artifact Removal From Sleep-Disordered EEG by Wavelet Enhanced Independent Component Analysis
DownloadFall 2024
In the field of sleep research, the quantitative analysis of electroencephalography (EEG) data acquired during sleep offers invaluable insights. However, the presence of artifacts in such data can severely distort analytical outcomes. Therefore, this study aims to develop an innovative artifact...
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Spring 2024
This dissertation is concerned with the parameter estimation problem for Ornstein-Uhlenbeck processes and Vasicek models and the product formula for multiple Itˆo integrals of L´evy processes. In the first part of the thesis, we study the parameter estimation for Ornstein- Uhlenbeck processes...