Related papers: Practical Valid Inferences for the Two-Sample Bino…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for…
The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random,…
Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
Introduction: estimation of confidence intervals (CIs) of binomial proportions has been reviewed more than once but the directional interpretation, distinguishing the overestimation from the underestimation, was neglected while the sample…
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…
The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
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,…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Traditional hypothesis tests for differences between binomial proportions are at risk of being too liberal (Wald test) or overly conservative (Fisher's exact test). This problem is exacerbated in small samples. Regulators favour exact…
The customary use of P-values in scientific research has been attacked as being ill-conceived, and the utility of P-values has been derided. This paper reviews common misconceptions about P-values and their alleged deficits as indices of…
Replicability is a lynchpin for credible discoveries. The partial conjunction (PC) p-value, which combines individual base p-values from multiple similar studies, can gauge whether a feature of interest exhibits replicated signals across…
We consider the problem of comparing two Poisson parameters from the Bayesian perspective. Kawasaki and Miyaoka (2012b) proposed the Bayesian index $P(\lambda_1 < \lambda_2 | X_1,X_2)$ and expressed it using the hypergeometric series. In…
Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal…