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Abstract:
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In physics, searches for new particles or new phenomena are mainly conducted via multiple hypothesis testing. Separate tests of hypothesis are implemented at different locations producing an ensemble of local p-values, and the smallest is reported as evidence for the new emission, once adequately adjusted to control the false detection rate. An alternative way to tackle the problem in statistical terms is via Tesing One Hypothesis Multiple times (TOHM). A stochastic process indexed by the various alternatives is used to combine the outcomes of each tests into a single global p-value, that can be used as as overall standard of evidence. The resulting statistical tool is particularly well suited for searches in high energy physics, where the significance level necessary to claim a discovery is usually of order of $5\sigma$. Specifically, TOHM targets the identification of rare signals, and provides valid inference with respect to stringent significance requirements, without encountering the problem of over-conservativeness.
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