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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
Thanks to the advancement of data-collecting technology in brain imaging, genomics, financial econometrics, and machine learning, scientific data tend to grow in both size and structural complexity, which are not amenable to traditional...
A major objective in modern human genetics research is to better understand the molecular mechanisms underlying human complex traits. Although genome-wide association studies (GWASs) have been successful in detecting thousands of trait...
Genome-wide association studies (GWAS) have significantly contributed to the identification of genetic variants by leveraging thousands of loci associated with complex traits and diseases, leading to breakthroughs in human genetics...
It is common to encounter skewed response data in medicine, epidemiology and health care studies. Methodology needs to be devised to overcome the natural difficulties that occur in analyzing such data particularly when it is multivariate...
The pair correlation function is very commonly used in describing the degree of attraction or repulsion between points in stationary point processes. Non-stationary spatial point processes arise in many applications, and it would be...
Meta-analysis has been frequently used to combine findings from independent studies in many areas. Bayesian methods are an important set of tools for performing meta-analyses. They avoid some potentially unrealistic assumptions that are...
Dependence is one of the most important concepts in probability and statistics. To detect and measure dependency between response variables and predictors, various models have been constructed, from simple models like least square...
Convolutional Neural Networks (CNNs) are widely used and have an impressive performance in detecting and classifying objects. However, the CNN's performance is sensitive to variations in rotation, position or scaling of the objects to be...
This dissertation includes four research projects. The first two projects mainly focus on the depth method on temporal point process data. The third project is the depth method on spatial point process. This is an extension of the first...
Our view is that while some of the basic principles of data analysis are going to remain unchanged, others are to be gradually replaced with Geometry and Topology methods. Linear methods are still making sense for functional data...
To date, Object Data Analysis is the most inclusive type of data analysis, as far as the object spaces are concerned. It extends multivariate data analysis, landmark based shape analysis, and in the infinite dimensional case, it extends...
Object retrieval is used in many popular photo applications. For example, the iPhone photos application has a search bar where objects can be queried to find photos of the given object. The goal of this thesis is to test a novel...
Identifying influential observations in the data is desired to ensure proper inference and statistical analysis. Modern methods to identify influence cases uses cross-validation diagnostics based on the effect of deletion of i-th...
Ideas from the algebraic topology of studying object data are used to introduce a framework for using persistence landscapes to vectorized objects. These methods are applied to analyze data from The Cancer Imaging Archive (TCIA), using a...
As we routinely encounter high-throughput datasets in complex biological and environment research, developing novel models and methods for variable selection has received widespread attention. In this dissertation, we addressed a few key...
Tukey's depth offers a powerful tool for nonparametric inference and estimation but also encounters serious computational and methodological difficulties in modern statistical data analysis. This article studies how to generalize Tukey's...
A large number of tensor datasets have been appearing in modern scientific research, attracting much attention to the analysis of such datasets. Tensor data often have high dimensionality and tensor structure that contains extra...
Interest in online rating data has increased in recent years in which ordinal ratings of products or local businesses are provided by users of a website, such as Yelp! or Amazon. One source of heterogeneity in ratings is that users apply...
The study of point processes and the analysis of data which involves spatial point patterns are important topics in spatial statistics with a long history and a large literature. A relatively new sub-area within this is the statistical...
Meta-analysis has been a popular statistical tool to combine scientific findings from multiple studies addressing the same topic. Publication bias and heterogeneity are two critical issues that may influence the validity of the...
This dissertation presents some topics in spatial statistics and their application in biostatistics and environmental statistics. The field of spatial statistics is an energetic area in statistics. In Chapter 2 and Chapter 3, the goal is...
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