Related papers: Bayesian credible interval construction for Poisso…
Confidence intervals for a binomial parameter or for the ratio of Poisson means are commonly desired in high energy physics (HEP) applications such as measuring a detection efficiency or branching ratio. Due to the discreteness of the data,…
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…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
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…
We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…
This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…
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…
This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low statistics where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters,…
We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to observational-data situations which are…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…
A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…
In observational studies, instrumental variables estimation is greatly utilized to identify causal effects. One of the key conditions for the instrumental variables estimator to be consistent is the exclusion restriction, which indicates…
Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful…
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…