Related papers: Frequentist limit setting in effective field theor…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
Empirical Bayes methods offer valuable tools for a large class of compound decision problems. In this tutorial we describe some basic principles of the empirical Bayes paradigm stressing their frequentist interpretation. Emphasis is placed…
In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity…
While gravitational waves have not yet been measured directly, data analysis from detection experiments commonly includes an upper limit statement. Such upper limits may be derived via a frequentist or Bayesian approach; the theoretical…
Several statistics used by physicists to declare the signal observability over the background are compared. It is shown that the frequentist method of testing a precise hypothesis allows one to estimate the power value of criteria with…
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…
The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…
Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically…
The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive…
The method of obtaining confidence intervals on a subset of the total number of parameters (p) of a model used for fitting X-ray spectra is to perturb the best-fitting model until, for each parameter, a range is found for which the change…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…
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…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the…
The unified approach of Feldman and Cousins allows for exact statistical inference of small signals that commonly arise in high energy physics. It has gained widespread use, for instance, in measurements of neutrino oscillation parameters…
It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and…