Related papers: Simultaneous adjustment of bias and coverage proba…
We propose an adaptive confidence interval procedure (CIP) for the coefficients in the normal linear regression model. This procedure has a frequentist coverage rate that is constant as a function of the model parameters, yet provides…
In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction…
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…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
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…
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…
Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…
Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of…
Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…
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…
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…
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…
When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…
A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…
We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…