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The projected discovery and exclusion capabilities of particle physics and astrophysics/cosmology experiments are often quantified using the median expected $p$-value or its corresponding significance. We argue that this criterion leads to flawed results, which for example can counterintuitively project lessened sensitivities if the experiment takes more data or reduces its background. We discuss the merits of several alternatives to the median expected significance, both when the background is known and when it is subject to some uncertainty. We advocate for standard use of the exact Asimov significance $Z^{rm A}$ detailed in this paper.
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well know
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed Poisson p
Usually, equal time is given to measuring the background and the sample, or even a longer background measurement is taken as it has so few counts. While this seems the right thing to do, the relative error after background subtraction improves when m
In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using different instrume
We present a procedure for reconstructing particle cascades from event data measured in a high energy physics experiment. For evaluating the hypothesis of a specific physics process causing the observed data, all possible reconstructi