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Spring 2024

Xie, Xiaoqi

The mountain pine beetle (Dendroctonus ponderosae, Hopkins 1902), an invasive bark beetle native to North America, has expanded its habitat from central British Columbia to Northern Alberta. This expansion poses an immediate threat to jack pine forests, which extend from Alberta to Nova Scotia....

Spring 2024

Sharma, Neha

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...

Spring 2024

Pineau, Mark

We consider the Cauchy problem to the Magneto-Hydrodynamics Equations (MHD) in R^3, and present specific criteria for which its corresponding energy equality holds. Specifically, we show that very weak solutions to the MHD equations (in the distributional sense) satisfy the energy equality,...

Spring 2024

Roda, Weston

This thesis is based on four main studies. The first two studies present a detailed methodology for completing dynamical system parameter estimation using Bayesian inference. The next two studies are about using this methodology to investigate critical human immunodeficiency virus-1 therapeutic...

Spring 2024

Murasko, Noel

Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with zeros) and implicit dealiasing (mathematically accounting...

Spring 2024

Zeng, Zhaowei

Versal torsors arise as an important tool in algebraic groups and algebraic geometry for the universal perspective they provide on the behaviour and properties of other torsors under the same group. Two classic examples of versal torsors are con- structed from general linear groups and affine...

Fall 2024

Ding, Lei

This thesis presents a comprehensive exploration of social biases embedded within texts and Natural Language Processing (NLP) models. It develops innovative algorithms to evaluate and mitigate these biases, thereby enhancing the fairness and effectiveness of NLP applications. The initial phase of...

Fall 2024

Sun, Ke

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...

Fall 2024

Wu, Christopher

Selection markets describe markets in which people strategically ``select'' into certain options based on knowledge only they possess, and in doing so may communicate some of that knowledge. Examples include sick people buying more comprehensive health insurance contracts, talented students...

Fall 2024

Polavarapu, Achintya Raya

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...