Related papers: Efficient representations of upper limits and conf…
Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
Experimenters report an upper limit if the signal they are trying to detect is non-existent or below their experiment's sensitivity. Such experiments may be contaminated with a background too poorly understood to subtract. If the background…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
When searching for new physics effects, collaborations will often wish to publish upper limits and intervals with a lower confidence level than the threshold they would set to claim an excess or a discovery. However, confidence intervals…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…
When backgrounds are not well enough controlled to measure the value of some physical parameter, one may still obtain an upper limit on the parameter. A single experiment may have several detectors, each of which can alone be used to derive…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
We define some appropriate statistical quantities that indicate the physical significance (reliability) of confidence intervals in the framework of both Frequentist and Bayesian statistical theories. We consider the expectation value of the…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different…
We discuss a new method for setting limits on small signals in the presence of background noise. The method is based on a combination of a two dimensional confidence region and the large sample approximation to the likelihood ratio test…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…