Related papers: Clopper-Pearson Bounds from HEP Data Cuts
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
We show that it makes sense to coarse grain hadronic interactions such as $\pi\pi$ and $\pi N$ reactions following previous work on NN scattering. Moreover, if the interaction is taken to be given by chiral dynamics at long distances above…
The original frequentist approach for computing confidence intervals involves the construction of the confidence belt which provides a mapping of the observation in data into a subset of values for the parameter. There are different…
We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a second experiment yields a realization of…
We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…
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 exact lower bound on the probability of the occurrence of exactly one of $n$ random events each of probability $p$ is obtained.
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
When conducting large scale inference, such as genome-wide association studies or image analysis, nominal $p$-values are often adjusted to improve control over the family-wise error rate (FWER). When the majority of tests are null,…
The threshold pbar-p peak in BES data for J/\Psi to gamma-pbar-p may be fitted as a cusp. It arises from the well known threshold peak in pbar-p elastic scattering due to annihilation. Several similar examples are discussed. The PS185 data…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
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 article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…
We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit…
We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…
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…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…