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When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…
We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable…
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.…
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…
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…
The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks…
A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
Calculating the expected number of misclassified outcomes is a standard problem of particular interest for rare-event searches. The Clopper-Pearson method allows calculation of classical confidence intervals on the amount of…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported…
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 novel confidence interval estimator is proposed for the risk difference in noninferiority binomial trials. The confidence interval is consistent with an exact unconditional test that preserves the type-I error, and has improved power,…
Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald,…
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…
Sequential estimation of a probability $p$ by means of inverse binomial sampling is considered. For $\mu_1,\mu_2>1$ given, the accuracy of an estimator $\hat{p}$ is measured by the confidence level $P[p/\mu_2\leq\hat{p}\leq p\mu_1]$. The…