Statistical Models Commons^™

Developing An Alternative Way To Analyze Nanostring Data, Shu Shen

Theses and Dissertations--Statistics

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that …

Statistical Inference On Dynamical Systems, Hongyuan Wang

Theses and Dissertations--Statistics

The ordinary differential equation (ODE) is one representative and popular tool in modeling dynamical systems, which are widely implemented in physics, biology, economics, chemistry and biomedical sciences, etc. Because of the importance of dynamical systems in scientific studies, they are the main focuses of my dissertation.

The first chapter of the dissertation is introduction and literature review, which mainly focuses on numerical integration algorithms of ODEs that are difficult to solve analytically, as well as derivative-free optimization algorithms for the so-called inverse problem.

The second chapter is on the estimation method based on numerical solvers of differential equations. We start …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Continuous Time Multi-State Models For Interval Censored Data, Lijie Wan

Theses and Dissertations--Statistics

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.

Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was …

Black Cloud Randomization Test, Nicholas S. Vanni

Williams Honors College, Honors Research Projects

The Black Cloud Randomization Test looks at a nontraditional question and attempts to answer the question using unique statistics. The purpose of this paper is to apply what has been learned throughout the years and apply this knowledge to a final project. Data for this project follows an emergency room’s on call schedule, as well as the number of traumas that came in during each day shift. The project builds on what has been already learned and helps to open a different way of working with statistics. The project was coded in the R software. With different restrictions, there are …

Resolving Gnetum Evolutionary History, Angela Mcfadden

All Master's Theses

Gnetum are non-flowering seed plants of the tropics, indigenous to South America, Africa, and Asia. This group of about 40 species is fascinating to botanists because it shares distinctive morphological characteristics with flowering plants, such as broad leaves, woody stems, and flower-like strobili. There are still questions surrounding the relationships within the genus of Gnetum. With that in mind, I focused my work on generating phylogenetic hypotheses, using two molecular data sets: a concatenation of over 60 different chloroplast genes (66,815 base pairs), and the whole chloroplast genome (128,772 base pairs). This allowed me to compare the two phylogenies …

Dimension Reduction And Variable Selection, Hossein Moradi Rekabdarkolaee

Theses and Dissertations

High-dimensional data are becoming increasingly available as data collection technology advances. Over the last decade, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics, signal processing, and environmental studies. Statistical techniques such as dimension reduction and variable selection play important roles in high dimensional data analysis. Sufficient dimension reduction provides a way to find the reduced space of the original space without a parametric model. This method has been widely applied in many scientific fields such as genetics, brain imaging analysis, econometrics, environmental sciences, etc. …

Space-Time Modelling Of Emerging Infectious Diseases: Assessing Leptospirosis Risk In Sri Lanka, Cameron C F Plouffe

Theses and Dissertations (Comprehensive)

In this research, models were developed to analyze leptospirosis incidence in Sri Lanka and its relation to rainfall. Before any leptospirosis risk models were developed, rainfall data were evaluated from an agro-ecological monitoring network for producing maps of total monthly rainfall in Sri Lanka. Four spatial interpolation techniques were compared: inverse distance weighting, thin-plate splines, ordinary kriging, and Bayesian kriging. Error metrics were used to validate interpolations against independent data. Satellite data were used to assess the spatial pattern of rainfall. Results indicated that Bayesian kriging and splines performed best in low and high rainfall, respectively. Rainfall maps generated from …