Related papers: Comment on Frank Porter, "Confidence intervals for…

We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…

We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to infinity. The limit distribution is non-standard and differs…

In this work, we study non-parametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some…

This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that…

I proposed (8, 1, 3) that p values should be supplemented by an estimate of the false positive risk (FPR). FPR was defined as the probability that, if you claim that there is a real effect on the basis of p value from a single unbiased…

The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical…

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…

When searching for new physics effects, collaborations will often wish to publish upper limits and intervals with a lower confidence level than the threshold they would set to claim an excess or a discovery. However, confidence intervals…

Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…

Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…

Original paper: We revisit the probability that any two consecutive events in a Poisson process N on [0,t] are separated by a time interval which is greater than s(<t) (a particular scan statistic probability), and the closely related…

We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space.…

We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramer-von Mises type is proposed and its asymptotic behavior is studied. We show that under null…

Likelihood functions are ubiquitous in data analyses at the LHC and elsewhere in particle physics. Partly because "probability" and "likelihood" are virtual synonyms in everyday English, but crucially distinct in data analysis, there is…

Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…

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…