Event Details

Two short talks about open research problems, given by staff and postgraduate students, accessible to undergraduate students.

Speaker 1: Gaetano Romano (lecturer)

Title: An Introduction to Fast Online Changepoint Detection

Abstract: Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time n, it involves considering O(n) possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to O(log(n)). This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time n to approximately log(n).

Speaker 2: Tom Keany (PhD Student)

Title: Statistics Beyond Points in Euclidean Space

Abstract: Modern statistical challenges often involve data that departs from classical Euclidean structures. This talk explores two key scenarios: data residing on surfaces like manifolds and data that is actually functional or measure-valued rather than simple points. We'll examine methods for detecting and characterising manifold structure in high-dimensional data, such as dimension estimation, and the role of curvature in statistical models such as PCA and regression. We'll then transition to statistics in metric spaces and infinite dimensional Hilbert spaces, discussing the extension of classical techniques like PCA to functional data and the unique challenges posed by the statistics of random measures. Throughout, we'll highlight how these geometric and topological considerations fundamentally shape our statistical methodology.