Speaker
Description
We use the tools of topological data analysis to detect some features of random sets in order to detect outliers or do goodness of fit testing. Persistence diagram is a key object of our interest and we view it as an empirical measure. Statistical depth can be defined on that (random) measure, for example by using support functions of corresponding lift zonoid and applying methods for assigning depth to functional data. We also use the persistence diagram for testing goodness of fit to Boolean model using so called accumulated persistence functions as test functions for global envelope test and compare the results with other test functions such as capacity functional, support function of the lift zonoid and spherical contact distribution function. It seems like it is very useful tool in recognizing whether clustering or repulsiveness occurs and can be used for detecting outliers.
