Conformal multiple Monte Carlo testing with a view to spatial statistics

Abstract: Monte Carlo tests are popular for their convenience, as they allow the computation of valid p-values even when test statistics with known and tractable distributions are unavailable. When performing multiple Monte Carlo tests, it is essential to adjust the testing procedure to maintain control of the type I error, and some of such techniques pose requirements on the joint distribution of the p-values, for instance independence. A straightforward approach to get independent p-values, is to compute the p-values for each hypothesis in parallel, however, this imposes a substantial computational burden. We highlight in this work that the problem of testing multiple data samples against the same null hypothesis is an instance of conformal outlier detection. Leveraging this insight enables a more efficient multiple Monte Carlo testing procedure, avoiding excessive simulations while still ensuring exact control over the false discovery rate. Through numerical experiments on point patterns we investigate the performance of this proposed conformal multiple Monte Carlo testing (CMMCTest) procedure.

machine learningprobabilitystatistics theory

Audience: researchers in the discipline

Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk). Speakers are asked to prepare material for 35 minutes excluding questions from the audience.