اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUpper Limits from Counting Experiments with Multiple Pipelines
272
0
0.0
(
0
)
تأليف
Patrick J. Sutton
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 instruments, different event detection algorithms, or observations over multiple time intervals. We demonstrate how to generalize the classical frequentist upper limit calculation to the case where multiple counts of events are made over one or more time intervals using several (not necessarily independent) procedures. We show how different choices of the rank ordering of possible outcomes in the space of counts correspond to applying different levels of significance to the various measurements. We propose an ordering that is matched to the sensitivity of the different measurement procedures and show that in typical cases it gives stronger upper limits than other choices. As an example, we show how this method can be applied to searches for gravitational-wave bursts, where multiple burst-detection algorithms analyse the same data set, and demonstrate how a single combined upper limit can be set on the gravitational-wave burst rate.
قيم البحث
اقرأ أيضاً
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
rocess is subject to a Poisson distributed background with unknown mean.
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
ults, 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
n fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.
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
ore 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.
We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and show how to
extract the parameters of the underlying distribution based on a set of observations sampled from this distribution. We illustrate the performance of this framework with an example from gravitational-wave astrophysics, demonstrating that the mass ratio distribution of merging compact-object binaries can be extracted from Malmquist-biased observations with substantial measurement uncertainty.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
