Speaker: Piotr Kokoszka, Professor, Department of Statistics, Colorado State University

Title: Detection And Localization Of Changes In Panels Of Random Densities

Abstract: The talk focuses on change point detection and localization in a nonstandard data structure. Viral load measurements during a prolonged epidemic provide an emerging tool for monitoring its progress. These measurements  can be treated as independent scalar observations following a density; one density per day per region. The data can thus be treated as a panel of incompletely observed random densities that may change over time, for example, due to the emergence of a new virus variant, change in public health policy, or other changes whose cause may not be obvious at the time of the change. Motivated by such and similar data in other fields, we propose statistical methodology for identifying panel  components where statistically significant changes have occurred and estimating their time, which can be different for different components. Challenges to overcome include sparse (or no) observations on certain days in certain components and the constrained form of random densities, which cannot be treated as unconstrained elements of a Hilbert space. We propose a solution based on an application of Bayes spaces of densities and suitable tools of functional data analysis. Following the presentation of the motivating data and the method, the talk will discuss the theoretical framework.