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Applying Thompson Sampling to Online Hypothesis Testing

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Title: Applying Thompson Sampling to Online Hypothesis Testing
Author(s): Suominen, Henri
Contributor: University of Helsinki, Faculty of Science, none
Discipline: none
Degree program: Master's Programme in Mathematics and Statistics
Specialisation: Applied Mathematics
Language: English
Acceptance year: 2021
Online hypothesis testing occurs in many branches of science. Most notably it is of use when there are too many hypotheses to test with traditional multiple hypothesis testing or when the hypotheses are created one-by-one. When testing multiple hypotheses one-by-one, the order in which the hypotheses are tested often has great influence to the power of the procedure. In this thesis we investigate the applicability of reinforcement learning tools to solve the exploration – exploitation problem that often arises in online hypothesis testing. We show that a common reinforcement learning tool, Thompson sampling, can be used to gain a modest amount of power using a method for online hypothesis testing called alpha-investing. Finally we examine the size of this effect using both synthetic data and a practical case involving simulated data studying urban pollution. We found that, by choosing the order of tested hypothesis with Thompson sampling, the power of alpha investing is improved. The level of improvement depends on the assumptions that the experimenter is willing to make and their validity. In a practical situation the presented procedure rejected up to 6.8 percentage points more hypotheses than testing the hypotheses in a random order.
Keyword(s): Multiple Hypothesis Testing Online Hypothesis Testing Reinforcement Learning

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