Physical Sciences and Mathematics Commons^™

Stage-Specific Predictive Models For Cancer Survivability, Elham Sagheb Hossein Pour

Theses and Dissertations

Survivability of cancer strongly depends on the stage of cancer. In most previous works, machine learning survivability prediction models for a particular cancer, were trained and evaluated together on all stages of the cancer. In this work, we trained and evaluated survivability prediction models for five major cancers, together on all stages and separately for every stage. We named these models joint and stage-specific models respectively. The obtained results for the cancers which we investigated reveal that, the best model to predict the survivability of the cancer for one specific stage is the model which is specifically built for that …

Estimating The Selection Gradient Of A Function-Valued Trait, Tyler John Baur

Theses and Dissertations

Kirkpatrick and Heckman initiated the study of function-valued traits in 1989. How to estimate the selection gradient of a function-valued trait is a major question asked by evolutionary biologists. In this dissertation, we give an explicit expansion of the selection gradient and construct estimators based on two different samples: one consisting of independent organisms (the independent case), and the other consisting of independent families of equally related organisms (the dependent case).

In the independent case we first construct and prove the joint consistency of sieve estimators of the mean and covariance functions of a Gaussian process, based on previous developments …

Density Estimation For Lifetime Distributions Under Semi-Parametric Random Censorship Models, Carsten Harlass

Theses and Dissertations

We derive product limit estimators of survival times and failure rates for randomly right censored data as the numerical solution of identifying Volterra integral equations by employing explicit and implicit Euler schemes. While the first approach results in some known estimators, the latter leads to a new general type of product limit estimator. Plugging in established methods to approximate the conditional probability of the censoring indicator given the observation, we introduce new semi-parametric and presmoothed Kaplan-Meier type estimators. In the case of the semi-parametric random censorship model, i.e. the latter probability belonging to some parametric family, we study the strong …

Detecting Association Of Gene-Environment Interactions In Common And Rare Variants For Hypertension, Miguelangel Diaz Medina

Theses and Dissertations

Subsequent malignant neoplasms (SMNs) or secondary cancers are one of the most negative effects resulting from cancer treatment such as chemotherapy or radiation. Given the severity and high incidence of mortality faced by cancer survivors, it is critical that we understand the cause of SMNs so that preventive measures or intervention can be done for individuals facing a higher risk of SMN incidence. The purpose of this thesis is to test the efficacy of newly developed statistical methods used to identify gene-environment interactions that are associated with a specific disease, in this case, SMNs, considering both common and rare variants, …

Statistical Contributions To Operational Risk Modeling, Daoping Yu

Theses and Dissertations

In this dissertation, we focus on statistical aspects of operational risk modeling. Specifically, we are interested in understanding the effects of model uncertainty on capital reserves due to data truncation and in developing better model selection tools for truncated and shifted parametric distributions. We first investigate the model uncertainty question which has been unanswered for many years because researchers, practitioners, and regulators could not agree on how to treat the data collection threshold in operational risk modeling. There are several approaches under consideration—the empirical approach, the “naive” approach, the shifted approach, and the truncated approach—for fitting the loss severity distribution. …

Are We Missing The Forest For The Trees? Quantifying The Maintenance Of Diversity In Temperate Deciduous Forests, Kathryn Barry

Theses and Dissertations

One of the most pressing questions of community ecology is: Why do we have so many species? Over 100 hypotheses have been proposed to answer this question for woody plants over the past 70 years, yet there remains no consensus among community ecologists. In this dissertation, I explore the evidence supporting several different hypotheses (Chapter 1). I provide evidence that negative density dependence, where individuals perform poorly near members of their own species, may only be relevant for canopy tree species (Chapter 2). Understory species do not demonstrate negative density dependence while canopy trees demonstrate negative density dependence that increases …

Parameter Estimation For The Spatial Ornstein-Uhlenbeck Process With Missing Observations, Sami Cheong

Theses and Dissertations

Suppose we are collecting a set of data on a rectangular sampling grid, it is reasonable to assume that observations (e.g. data that arise in weather forecasting, public health and agriculture) made on each sampling site are spatially correlated. Therefore, when building a model for this type of data, we often pair it with an underlying Gaussian process that contains different spatially dependent parameters. Here, we assume that the Gaussian process is characterized by the Ornstein-Uhlenbeck covariance function, which has the property of being both stationary and Markov under the assumption that no observations are missing. However, in reality, the …

Comparing The Riskiness Of Dependent Portfolios, Ranadeera Gamage Madhuka Samanthi

Theses and Dissertations

A nonparametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a required condition for the test to work. In this dissertation, we investigate how the performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study where we consider three different risk measures: conditional tail expectation, proportional hazards transform, and mean. Further, three portfolios are generated from exponential, Pareto, and lognormal distributions, and …

Longitudinal Data Models With Nonparametric Random Effect Distributions, Hartmut Jakob Stenz

Theses and Dissertations

There is the saying which says you cannot see the woods for the trees. This

thesis aims to circumvent this unfortunate situation: Longitudinal data on

tree growth, as an example of multiple observations of similar individuals

pooled together in one data set, are modeled simultaneously rather than

each individual separately. This is done under the assumption that one

model is suitable for all individuals but its parameters vary following un-

known nonparametric random effect distributions. The goal is a maximum

likelihood estimation of these distributions considering all provided data and

using basis-spline-approximations for the densities of each distribution func-

tion …