Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions

Explore a 56-minute talk on topology-driven goodness-of-fit tests applicable to arbitrary dimensions. Delve into the adoption of the Euler characteristic curve (ECC) for conducting one- and two-sample goodness of fit tests, addressing limitations of classical tools like the Kolmogorov-Smirnov test in higher dimensions. Discover the TopoTests procedure, which offers comparable power to state-of-the-art tests in one-dimensional cases while extending to samples of any dimension. Learn about the controlled type I error and exponentially vanishing type II error of TopoTests as sample size increases. Examine extensive numerical simulations demonstrating the power of TopoTests for various sample sizes. Gain insights from this joint research work by Paweł Dłotko, Łukasz Stettner, and Rafał Topolnicki, as presented by Niklas Hellmer for the Applied Algebraic Topology Network.