Multiple testing in game-theoretic probability: pictures and questions
arxiv(2024)
摘要
The usual way of testing probability forecasts in game-theoretic probability
is via construction of test martingales. The standard assumption is that all
forecasts are output by the same forecaster. In this paper I will discuss
possible extensions of this picture to testing probability forecasts output by
several forecasters. This corresponds to multiple hypothesis testing in
statistics. One interesting phenomenon is that even a slight relaxation of the
requirement of family-wise validity leads to a very significant increase in the
efficiency of testing procedures. The main goal of this paper is to report
results of preliminary simulation studies and list some directions of further
research.
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