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Skip to Search Results 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Hillen, Thomas (Mathematical and Statistical Sciences)
 6Mizera, Ivan (Mathematical and Statistical Sciences)

Fall 2018
Approximation of probability measures, quantization, Kantorovich metric, Levy metric, Kolmogorov metric, Benford's Law, slowly changing sequences, asymptotic distribution, invariance property.","This thesis is based on four papers. The first two papers fall into the field of approximation of...

Fall 2015
In this thesis, we present expositions of GromovWitten invariants, Hurwitz numbers, topological recursion and their connections. By remodeling theory, open GromovWitten invariants of C^3 and C^3/Za satisfy the topological recursion of EynardOrantin defined on framed mirror curve of toric...

Fall 2014
Among representation theorists, it is well known that Yangians can be realized as some type of degenerate form of quantum loop algebras. What is not well known is precisely how this degeneration takes place. In the first part of this thesis, we will demonstrate explicitly the process by which...

Spring 2016
In this thesis, we first introduce two basic problems of filter, the nonlinear filtering and model selection problem. We show that both of them can be solved by the unnormalized filter approach. Then several web based particle filter algorithms will be discussed. We extend the resampled and...

Theoretical and Computational Aspects of Mixture Models, with Applications to Empirical Bayes Methods
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This thesis studies mixture models, in particular the estimation of mixing distributions and their applications to empirical Bayes prediction. The objectives are twofold: to study the largesample property of empirical Bayes estimators; to develop algorithms for the nonparametric estimation of...

Fall 2011
Cancer is one of the major causes of death in the world. In the field of Oncology, clinical trials form the crux of medical effort to find better treatment schedules. These trials are expensive, time consuming, and carry great risks for the patients involved. Mathematical models provide a...

Spring 2013
Imposing constraints on the class of the available selffinancing strategies may eliminate the possibility of using replicating or superhedging strategies, which leads to the problem of partial hedging. In the present work, the partial hedging problem is investigated from the viewpoint of the...

Fall 2020
Formation of singularities in physical phenomena has always fascinated scientists and stimulated both development of mathematical theories accounting for observations and further experimental scrutiny of the governing physics with the goal to resolve the singular behavior. The underlying theme of...

Fall 2009
Informative random censoring survival data are often seen in clinical trials. However, the methodology to deal with this kind of data has not been well developed due to difficulty of identifying the information. Several methods were proposed, for example, by \citet{Sia1}. We use simulation...

Spring 2017
We explore the connection between EynardOrantin Topological Recursion (EOTR) and the asymptotic solutions to differential equations constructed with the WKB method (named for its creators Wentzel, Kramers and Brillouin). Using the Airy spectral curve as an initial example, we propose a general...