Statistics and Probability Commons^™

A Comparative Spatial And Climate Analysis Of Human Granulocytic Anaplasmosis And Human Babesiosis In New York State (2013-2018), Collin J. O'Connor

Legacy Theses & Dissertations (2009 - 2024)

Human granulocytic anaplasmosis (HGA) and human babesiosis are tick-borne diseases spread by Ixodes scapularis (the blacklegged or deer tick) and are the result of infection with Anaplasma phagocytophilum and Babesia microti, respectively. In New York State (NYS), incidence rates of these diseases increased concordantly until around 2013, when rates of HGA began to increase more rapidly than human babesiosis, and the spatial extent of the diseases diverged. Surveillance data of tick-borne pathogens (2007 to 2018) and reported human cases of HGA (n=4,297) and human babesiosis (n=2,986) (2013 to 2018) from the New York State Department of Health (NYSDOH) showed a …

Three Essays On Model Selection, Fangning Li

Legacy Theses & Dissertations (2009 - 2024)

In empirical research, we often need to address the issue of what model to use given a collection of candidate models. Conventionally, we use model selection to choose one best model from the collection of candidate models based on some model selection criteria. Model averaging is a generalization of model selection in the sense that it assigns weights to candidate models and uses a weighted average to construct an aggregated model. Usually model averaging provides better performance than model selection which chooses a single candidate model based on AIC or BIC.

Parsimonious Covariate Selection For Interval Censored Data, Yi Cui

Legacy Theses & Dissertations (2009 - 2024)

Interval censored outcomes widely arise in many clinical trials and observational studies. In many cases, subjects are only followed-up periodically. As a result, the event of interest is known only to occur within a certain interval. We provided a method to select the parsimonious set of covariates associated with the interval censored outcome. First, the iterative sure independence screening (ISIS) method was applied to all interval censored time points across subjects to simultaneously select a set of potentially important covariates; then multiple testing approaches were used to improve the selection accuracy through refining the selection criteria, i.e. determining a refined …

An Analysis Of Income And Other Associative Demographics To Charity Donation And Volunteerism, Christine Lynn Klotz

Legacy Theses & Dissertations (2009 - 2024)

Nongovernmental organizations have a vast institutional presence across the United States. Each year, there is an ever-increasing body of charitable organizations which span, enhance and characterize the civil sphere. Overall, charities occupy an important institutional role in society, and the individuals who help to sustain charities encompass a vital social role. This paper is particularly concerned with analyzing charitable donation and volunteering dynamics on the individual level. Using the 2014 General Social Survey data on charitableness, this paper estimates the probability of engaging in volunteerism and charitable donation within the nonprofit sector based on income level. These results suggest that …

Aggregate Loss Model With Poisson-Tweedie Loss Frequency, Si Chen

Theses and Dissertations (Comprehensive)

The aggregate loss model has applications in various areas such as financial risk management and actuarial science. The aggregate loss is the summation of all random losses occurred in a period, and it is governed by both the loss severity and the loss frequency. While the impact of the loss severity on aggregate loss is well studied, less focus is paid on the influence of loss frequency on aggregate loss, which motivates our study. In this thesis, we enrich the aggregate loss framework by introducing the Poisson-Tweedie distribution as a candidate for modelling loss frequency, prove the closedness of Poisson-Tweedie …

Quantifying Effects Of Sleep Deprivation On Cognitive Performance, Quang Nghia Le

Masters Theses

“The most commonly used metric for evaluating alertness and vigilance is the Psychomotor Vigilance Test (PVT), previous studies have indicated that alertness and vigilance can be affected by the lack of sleep as a function of sleep loss. This study explores methods to predict median psychomotor vigilance reaction times. The data used in this study comes from a series of tests and surveys conducted on volunteer students. The data set contains many potential predictors of PVT and one aspect of the study was to identify variables that are useful in prediction. The performances of various prediction methods that allow for …

Teaching Introductory Statistics With Datacamp, Benjamin Baumer, Andrew P. Bray, Mine Çetinkaya-Rundel, Johanna S. Hardin

Statistical and Data Sciences: Faculty Publications

We designed a sequence of courses for the DataCamp online learning platform that approximates the content of a typical introductory statistics course. We discuss the design and implementation of these courses and illustrate how they can be successfully integrated into a brick-and-mortar class. We reflect on the process of creating content for online consumers, ruminate on the pedagogical considerations we faced, and describe an R package for statistical inference that became a by-product of this development process. We discuss the pros and cons of creating the course sequence and express our view that some aspects were particularly problematic. The issues …

An Assessment Of Convergence In The Feeding Morphology Of Xiphactinus Audax And Megalops Atlanticus Using Landmark-Based Geometric Morphometrics, Edward Chase Shelburne

Master's Theses or Doctor of Nursing Practice

Convergence is an evolutionary phenomenon wherein distantly related organisms independently develop features or functional adaptations to overcome similar environmental constraints. Historically, convergence among organisms has been speculated or asserted with little rigorous or quantitative investigation. More recent advancements in systematics has allowed for the detection and study of convergence in a phylogenetic context, but this does little to elucidate convergent anatomical features in extinct taxa with poorly understood evolutionary histories. The purpose of this study is to investigate one potentially convergent system—the feeding structure of Xiphactinus audax (Teleostei: Ichthyodectiformes) and Megalops atlanticus (Teleostei: Elopiformes)—using a comparative anatomical approach to assess …

Novel Random Forest Methods And Algorithms For Autism Spectrum Disorders Research, Afrooz Jahedi

CGU Theses & Dissertations

Random Forest (RF) is a flexible, easy to use machine learning algorithm that was proposed by Leo Breiman in 2001 for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Its superior prediction accuracy has made it the most used algorithms in the machine learning field. In this dissertation, we use the random forest as the main building block for creating a proximity matrix for multivariate matching and diagnostic classification problems that are used for autism research (as an exemplary application). In observational studies, matching is used to optimize the balance …

How We Can Extend The Standard Deviation Notion With Neutrosophic Interval And Quadruple Neutrosophic Numbers, Victor Christianto, Florentin Smarandache, Muhammad Aslam

Branch Mathematics and Statistics Faculty and Staff Publications

During scientific demonstrating of genuine specialized framework we can meet any sort and rate model vulnerability. Its reasons can be incognizance of modelers or information mistake. In this way, characterization of vulnerabilities, as for their sources, recognizes aleatory and epistemic ones. The aleatory vulnerability is an inalienable information variety related with the researched framework or its condition. Epistemic one is a vulnerability that is because of an absence of information on amounts or procedures of the framework or the earth [7]. Right now, we examine fourfold neutrosophic numbers and their potential application for practical displaying of physical frameworks, particularly in …

Nonparametric False Discovery Rate Control For Identifying Simultaneous Signals, Sihai Dave Zhao, Yet Tian Nguyen

Mathematics & Statistics Faculty Publications

It is frequently of interest to identify simultaneous signals, defined as features that exhibit statistical significance across each of several independent experiments. For example, genes that are consistently differentially expressed across experiments in different animal species can reveal evolutionarily conserved biological mechanisms. However, in some problems the test statistics corresponding to these features can have complicated or unknown null distributions. This paper proposes a novel nonparametric false discovery rate control procedure that can identify simultaneous signals even without knowing these null distributions. The method is shown, theoretically and in simulations, to asymptotically control the false discovery rate. It was also …

Statistical Analysis Of Fnirs Data: Consideration Of Spatial Varying Coefficient Model Of Prefrontal Cortex Activity Changes During Speech Motor Learning In Apraxia Of Speech, Rachel Johnson, Jennifer Matthews, Norou Diawara, Rachel Carroll

Communication Disorders & Special Education Faculty Publications

Apraxia of speech is an impairment in the planning and programming of speech typically accompanied by aphasia (language impairment) secondary to a left hemisphere stroke. It is unknown if the structural and functional connections to the damaged area implicate the integrity of the cognitive functions of the prefrontal cortex (PFC). The present study examines the feasibility of measuring hemodynamic activity in the PFC in response to the structure of practice and during treatment. This multiple-baseline single case-design study involving two individuals with chronic acquired apraxia of speech measured the hemodynamic changes in PFC activity during treatment across the intervention period …

Algebraic And Geometric Properties Of Hierarchical Models, Aida Maraj

Theses and Dissertations--Mathematics

In this dissertation filtrations of ideals arising from hierarchical models in statistics related by a group action are are studied. These filtrations lead to ideals in polynomial rings in infinitely many variables, which require innovative tools. Regular languages and finite automata are used to prove and explicitly compute the rationality of some multivariate power series that record important quantitative information about the ideals. Some work regarding Markov bases for non-reducible models is shown, together with advances in the polyhedral geometry of binary hierarchical models.

Unitary And Symmetric Structure In Deep Neural Networks, Kehelwala Dewage Gayan Maduranga

Theses and Dissertations--Mathematics

Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well-known difficulty in using RNNs is the vanishing or exploding gradient problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN), which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the …

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, Kyle Eric Helfrich

Theses and Dissertations--Mathematics

Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this work we describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue, and derive update schemes for each architecture. Another portion of this work focuses on the often used technique of batch normalization. Although found to be successful …

Cancer Phylogenetic Analysis Based On Rna-Seq Data, Tingting Zhai

Theses and Dissertations--Statistics

Studying tumor evolution is a major task to understand the biological mechanism of carcinogenesis, develop new cancer therapies, and prevent drug resistance. We focus on two important questions in tumor evolution. The first question is to quantify intra-tumor heterogeneity, where multiple subclones of tumor cells with distinct transcriptomic profiles. Another question is to estimate the temporal order of alteration of key cancer pathways during tumor evolution. We present a new statistical method to 1) reconstruct the evolutionary history and population frequency of the subclonal lineages of tumor cells and 2) infer temporal order of pathway alterations in tumor evolution for …

Semiparametric And Nonparametric Methods For Comparing Biomarker Levels Between Groups, Yuntong Li

Theses and Dissertations--Statistics

Comparing the distribution of biomarker measurements between two groups under either an unpaired or paired design is a common goal in many biomarker studies. However, analyzing biomarker data is sometimes challenging because the data may not be normally distributed and contain a large fraction of zero values or missing values. Although several statistical methods have been proposed, they either require data normality assumption, or are inefficient. We proposed a novel two-part semiparametric method for data under an unpaired setting and a nonparametric method for data under a paired setting. The semiparametric method considers a two-part model, a logistic regression for …

Estimation Of The Treatment Effect With Bayesian Adjustment For Covariates, Li Xu

Theses and Dissertations--Statistics

The Bayesian adjustment for confounding (BAC) is a Bayesian model averaging method to select and adjust for confounding factors when evaluating the average causal effect of an exposure on a certain outcome. We extend the BAC method to time-to-event outcomes. Specifically, the posterior distribution of the exposure effect on a time-to-event outcome is calculated as a weighted average of posterior distributions from a number of candidate proportional hazards models, weighing each model by its ability to adjust for confounding factors. The Bayesian Information Criterion based on the partial likelihood is used to compare different models and approximate the Bayes factor. …

Nonparametric Analysis Of Clustered And Multivariate Data, Yue Cui

Theses and Dissertations--Statistics

In this dissertation, we investigate three distinct but interrelated problems for nonparametric analysis of clustered data and multivariate data in pre-post factorial design.

In the first project, we propose a nonparametric approach for one-sample clustered data in pre-post intervention design. In particular, we consider the situation where for some clusters all members are only observed at either pre or post intervention but not both. This type of clustered data is referred to us as partially complete clustered data. Unlike most of its parametric counterparts, we do not assume specific models for data distributions, intra-cluster dependence structure or variability, in effect …

Nonparametric Tests Of Lack Of Fit For Multivariate Data, Yan Xu

Theses and Dissertations--Statistics

A common problem in regression analysis (linear or nonlinear) is assessing the lack-of-fit. Existing methods make parametric or semi-parametric assumptions to model the conditional mean or covariance matrices. In this dissertation, we propose fully nonparametric methods that make only additive error assumptions. Our nonparametric approach relies on ideas from nonparametric smoothing to reduce the test of association (lack-of-fit) problem into a nonparametric multivariate analysis of variance. A major problem that arises in this approach is that the key assumptions of independence and constant covariance matrix among the groups will be violated. As a result, the standard asymptotic theory is not …