Related papers: Confidence limits: what is the problem? Is there t…
One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
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…
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…
Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This…
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…
We study the frequentist properties of confidence intervals for the On-Off problem. The methods include all those in common use today. We derive explicit formulas for the limits and calculate the true coverage and the expected lengths of…
Building a safety case is a common approach to make expert judgement explicit about safety of a system. The issue of confidence in such argumentation is still an open research field. Providing quantitative estimation of confidence is an…
We show that the unified method recently proposed by Feldman and Cousins to put confidence intervals on bounded parameters cannot avoid the possibility of getting null results. A modified bayesian approach is also proposed (although not…
In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…
Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…
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…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
Various measures can be used to estimate bias or unfairness in a predictor. Previous work has already established that some of these measures are incompatible with each other. Here we show that, when groups differ in prevalence of the…