Parsimonious high-dimensional and matrix-variate copula modeling

With technology yielding larger and more diverse data collections, many scientific domains seek innovative ways to investigate "big data". Although statistical methods are the standard scientific procedure for analyzing and interpreting data, many of the standard approaches cannot be used to analyze big data. This inability can be due to large computational burdens, or in some cases, the standard methods cannot be extended to handle large numbers of variables. This proposed research will develop novel methods for the assignment of observations in big data to groups based on commonalities, without any prior knowledge of the correct grouping. This procedure is called clustering and is a type of unsupervised learning method as it does not assume prior knowledge of the correct assignments or even the number of groups. Clustering is used to identify underlying structures and patterns in the data and may be used to localize analyses into groups. This research will focus on developing innovative clustering methods to analyze data with many recorded variables that have socio-economic and environmental importance (e.g., gene expression, economic, health, and geo-referenced spatial data) as well as three-way data (e.g., gray-scale images and multiple variables recorded over time aka "longitudinal data"). This work will advance our understanding in the use of clustering to model big data. Methods developed will be presented in freely available statistical software packages in R for use by practitioners and researchers. This research will impact the analysis of big data in diverse fields including medicine, economics, marketing, food science, biology, and environmental sciences.