ﻻ يوجد ملخص باللغة العربية
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 more time is spent counting the measurement with the highest amount of scattering. As the available measurement time is always limited, a good division must be found between measuring the background and sample, so that the uncertainty of the background-subtracted intensity is as low as possible. Herein outlined is the method to determine how best to divide measurement time between a sample and the background, in order to minimize the relative uncertainty. Also given is the relative reduction in uncertainty to be gained from the considered division. It is particularly useful in the case of scanning diffractometers, including the likes of Bonse-Hart cameras, where the measurement time division for each point can be optimized depending on the signal-to-noise ratio.
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
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
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
The current and upcoming generation of Very Large Volume Neutrino Telescopes---collecting unprecedented quantities of neutrino events---can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass or