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We propose a method for setting limits that avoids excluding parameter values for which the sensitivity falls below a specified threshold. These power-constrained limits (PCL) address the issue that motivated the widely used CLs procedure, but do so in a way that makes more transparent the properties of the statistical test to which each value of the parameter is subjected. A case of particular interest is for upper limits on parameters that are proportional to the cross section of a process whose existence is not yet established. The basic idea of the power constraint can easily be applied, however, to other types of limits.
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
The question of exclusion region construction in new phenomenon searches has been causing considerable discussions for many years and yet no clear mathematical definition of the problem has been stated so far. In this paper we formulate the problem i
Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDFs) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is related to the in
Measurements are inseparable from inference, where the estimation of signals of interest from other observations is called an indirect measurement. While a variety of measurement limits have been defined by the physical constraint on each setup, the
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial bounds on the me