Project topic posted by Pat Morin

2-Dimensional Depth Algorithms

Data depth is a field of statistics where one tries to assign, for each point in Rd a depth that describes how deep that point is with respect to some distribution or set of observations. Once a depth function is defined then a number of computational questions arise: 1. How do we compute the depth of a point p in a set S? 2. How do we find the point p* of maximum depth? 3. How can we compute the contour of all points whose depth is bigger than some value? There are many definitions of depth for which the answers to these three questions are not yet known. In other cases, efficient algorithms have been proposed, but there are still no implementations of these algorithms.

The goal of this project is to develop efficient algorithms for solving depth problems in 2 dimensions and to implement these algorithms in a data depth library.