Related papers: A computed 95% confidence interval does cover the …
Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…
In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…
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…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
The precise value of the neutron lifetime is of fundamental importance to particle physics and cosmology. The neutron lifetime recently obtained, 878.5 +/- 0.7stat +/- 0.3sys s, is the most accurate one to date. The new result for the…
Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This…
This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that…
Confidence intervals are assessed according to two criteria, namely expected length and coverage probability. In an attempt to apply the decision-theoretic method to finding a good confidence interval, a loss function that is a linear…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the…
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…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…
Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model…
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…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…
Accurate battery lifetime prediction is important for preventative maintenance, warranties, and improved cell design and manufacturing. However, manufacturing variability and usage-dependent degradation make life prediction challenging.…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…
We consider a linear regression model with regression parameter beta =(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…