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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 process is subject to a Poisson distributed background with unknown mean.
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
Several experiments in high-energy physics and astrophysics can be treated as on/off measurements, where an observation potentially containing a new source or effect (on measurement) is contrasted with a background-only observation free of the effect
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 res
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
One of the most popular lottery games worldwide is the so-called ``lotto k/N. It considers N numbers 1,2,...,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those player