Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Conditional minimum volume predictive regions for stochastic processes

Abstract: Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume predictor (MV-predictor) for a strictly stationary process. The MV-predictor varies with respect to the current position in the state space and has the minimum Lebesgue measure among all regions with the nominal coverage probability. We have established consistency, convergence rates, and asymptotic normality for both coverage probability and Lebesgue measure of the estimated MV-predictor under the assumption that the observations are taken from a strong mixing process. Applications with both real and simulated data sets illustrate the proposed methods.

Confidence intervals for proportions estimated by group testing with groups of unequal size

Abstract: Group testing, in which units are pooled together and tested as a group for the presence of an attribute, has been used in many fields of study, including blood testing, plant disease assessment, fisheries, and vector transmission of viruses. When groups are of unequal size, complications arise in the derivation of confidence intervals for the proportion of units in the population with the attribute. We evaluate several asymptotic interval estimation methods for problems in which groups are of different size. Each method is examined for its theoretical properties, and adapted or developed for group testing. In an initial assessment using a study of virus prevalence in carnations, four methods are found to be satisfactory, and are considered further—two based on the distribution of the MLE, one on the score statistic, and one on the likelihood ratio. The performance of each method is then tested empirically on five realistic group testing procedures, with the evaluation focusing on the coverage probability provided by the confidence intervals. A method based on the score statistic with a correction for skewness is recommended, followed by a method in which the logit function is applied to the MLE.

Inference in infinite-dimensional inverse problems: Discretization and duality

Abstract: Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.