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A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
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…
Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the…
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…
There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We…
We discuss a new method for setting limits on small signals in the presence of background noise. The method is based on a combination of a two dimensional confidence region and the large sample approximation to the likelihood ratio test…
Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…
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…
The paper comments on properties of the so-called "Unified approach to the construction of classical confidence intervals", in which confidence intervals are computed in a Neyman construction using the likelihood ratio as ordering quantity.…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
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 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…
We present an optimization-based framework to construct confidence intervals for functionals in constrained inverse problems, ensuring valid one-at-a-time frequentist coverage guarantees. Our approach builds upon the now-called strict…
The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…
This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a…
Don Fraser has given an interesting account of the agreements and disagreements between Bayesian posterior probabilities and confidence levels. In this comment I discuss some cases where the lack of such agreement is extreme. I then discuss…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
I present a frequentist method for quantifying uncertainty when correcting correlations for attenuation due to measurement error. The method is conservative but has far better coverage properties than the methods currently used when sample…
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…