Testing imprecise hypotheses

Speaker: Lucas Kania, Carnegie Mellon University

Abstract: In modern scientific applications, practitioners are interested in testing theories that are not fully specified or might be partially misspecified. That is, there is a need to allow for a certain amount of imprecision when testing a null hypothesis. Tolerant testing offers a particular solution to the problem: practitioners state a simple null hypothesis and indicate how much deviation from it should be tolerated when testing it. In this talk, I will discuss how the amount of allowed imprecision affects the hardness of the problem. If time allows, I will explain how the hardness of the problem is deeply connected to the best polynomial approximation of certain functions. This talk is based on joint work with Tudor Manole (MIT), Sivaraman Balakrishnan (CMU), and Larry Wasserman (CMU).

Biography: Lucas Kania is a PhD student in statistics at Carnegie Mellon University. Previously, he worked with Prof. Ernst Wit on out-of-sample risk guarantees at the Statistical Computing Laboratory, under Prof. Marco Zaffalon and Dr. Dario Azzimonti on scaling Sparse Gaussian Processes at IDSIA, and with Prof. Kai Hormann on exact root finding.

Host: Prof. Ernst Wit