Parallel Computation of Bivariate Point Data Depths and Display of Intrinsic Depth Segments

Data depth is a central topic in order statistics and data analysis. However, the increasing needs of massive data sets and the related high costs of running algorithms pose challenges for statisticians and data analysts. First, this dissertation presents a new way to compute simplicial and Tukey data depths using Open Multi-Processing parallelization. We show that it is practical to compute point depths for tens of thousands of points. The definition of point depth is the order statistic depth of a single point, here in two dimensions. Second, using the point depths, we explore the regional depth characteristics of the data set as a whole. Using this new methodology, fast parallel computation of both simplicial depth and Tukey depth for a data set of n points has time complexity of O(n^2 log n) with O(n) space, which is practical for n up to 100,000. Obtaining depths for a large number of points in a faster manner by parallel computation supports identifying the central region quickly, since the points of maximum depth are known. The point depth computation identifies the depths of selected spoke segments around each origin point. These spoke depths are used to create new visualizations of depth characteristics and contour depths without adding virtual points