Multiple testing in game-theoretic probability: pictures and questions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916164032004096 |
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| author | Vovk, Vladimir |
| author_facet | Vovk, Vladimir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_11767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple testing in game-theoretic probability: pictures and questions Vovk, Vladimir Methodology 62L10 (Primary) 62F03, 62G10, 60G42, 62A01 (Secondary) 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. |
| title | Multiple testing in game-theoretic probability: pictures and questions |
| topic | Methodology 62L10 (Primary) 62F03, 62G10, 60G42, 62A01 (Secondary) |
| url | https://arxiv.org/abs/2403.11767 |