Related papers: Simple Buehler-optimal confidence intervals on the…
Interval estimation of the probability of success in a Binomial model is considered. Zieli\'nski (2018) showed that the confidence interval which uses information about non-homogeneity of the sample is better than the classical one. In the…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains 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…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
In this short note I apply the methodology of game-theoretic probability to calculating non-asymptotic confidence intervals for the coefficient of a simple first order scalar autoregressive model. The most distinctive feature of the…
Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…
The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the…
We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
Suppose that X_1,X_2,...,X_n are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-\alpha/2 upper confidence interval and a…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
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…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…