Related papers: Treatment of the background error in the statistic…
We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-\beta' \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha'. We show that this…
A results of numerical procedure for construction of confidence intervals for parameter of Poisson distribution for signal in the presence of background which has Poisson distribution with known value of parameter are presented. It is shown…
The evaluation of the error to be attributed to cut efficiencies is a common question in the practice of experimental particle physics. Specifically, the need to evaluate the efficiency of the cuts for background removal, when they are…
In this paper we propose a procedure to evaluate Bayesian confidence intervals in counting experiments where both signal and background fluctuations are described by the Poisson statistics. The results obtained when the method is applied to…
Expected coverage and expected length of 90% upper and lower limit and 68.27% central intervals are plotted as functions of the true signal for various values of expected background. Results for several objective priors are shown, and…
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented. Introducing the conditional probability satisfying the…
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…
Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…
In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties.…
We propose using a Bayes procedure with uniform improper prior to determine credible belts for the mean of a Poisson distribution in the presence of background and for the continuous problem of measuring a non-negative quantity $\theta$…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
The incorporation of uncertainties to calculations of signal significance in planned experiments is an actual task. Several approaches to this problem are discussed. We present a procedure for taking into account the systematic uncertainty…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
Given data from a Poisson point process with intensity $(x,y) \mapsto n \mathbf{1}(f(x)\leq y),$ frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson…
Hypothesis tests for the presence of new sources of Poisson counts amidst background processes are frequently performed in high energy physics (HEP), gamma ray astronomy (GRA), and other branches of science. While there are conceptual…
The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the…
We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…
The problem of inferring the binomial parameter p from x successes obtained in n trials is reviewed and extended to take into account the presence of background, that can affect the data in two ways: a) fake successes are due to a…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
We present a procedure for calculating an upper limit on the number of signal events which incorporates the Poisson uncertainty in the background, estimated from control regions of one or two dimensions. For small number of signal events,…