Coverage probability

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

A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

Abstract: The problem of finding confidence intervals for the success parameter of a binomial experiment has a long history, and a myriad of procedures have been developed. Most exploit the duality between hypothesis testing and confidence regions and are typically based on large sample approximations. We instead employ a direct approach that attempts to determine the optimal coverage probability function a binomial confidence procedure can have from the exact underlying binomial distributions, which in turn defines the associated procedure. We show that a graphical perspective provides much insight into the problem. Both procedures whose coverage never falls below the declared confidence level and those that achieve that level only approximately are analyzed. We introduce the Length/Coverage Optimal method, a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and show that it is superior in important ways to existing procedures.

The Effect of Dependence on Confidence Intervals for a Population Proportion

Abstract: The binomial model is widely used in statistical applications. Usually, the success probability, p, and its associated confidence interval are estimated from a random sample. Thus, the observations are independent and identically distributed. Motivated by a legal case where some grand jurors could serve a second year, this article shows that when the observations are dependent, even slightly, the coverage probabilities of the usual confidence intervals can deviate noticeably from their nominal level. Several modified confidence intervals that incorporate the dependence structure are proposed and examined. Our results show that the modified Wilson, Agresti-Coull, and Jeffreys confidence intervals perform well and can be recommended for general use.

Modeling Infrastructure Sharing in mmWave Networks With Shared Spectrum Licenses

Abstract: Competing cellular operators aggressively share infrastructure in many major US markets If operators were also to share spectrum in next-generation millimeter-wave (mmWave) networks, intra-network interference will become correlated with inter-network interference We propose a mathematical framework to model a multi-operator mmWave cellular network with co-located base-stations (BSs) We then characterize the signal-to-interference-plus-noise ratio distribution for an arbitrary network and derive its coverage probability To understand how varying the spatial correlation between different networks affects coverage probability, we derive special results for the two-operator scenario, where we construct the operators’ individual networks from a single network via probabilistic coupling For external validation, we devise a method to quantify and estimate spatial correlation from actual BS deployments We compare our two-operator model against an actual macro-cell-dominated network and an actual network primarily comprising distributed-antenna-system (DAS) nodes Using the actual deployment data to set the parameters of our model, we observe that coverage probabilities for the model and actual deployments not only compare very well to each other, but also match nearly perfectly for the case of the DAS-node-dominated deployment Another interesting observation is that a network that shares spectrum and infrastructure has a lower rate coverage probability at low rate thresholds than a network of the same number of BSs that shares neither spectrum nor infrastructure, suggesting that the latter is more suitable for low-rate applications

Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses.

Abstract: Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of inter...

Load Forecasting and Neural Networks: A Prediction Interval-Based Perspective

Abstract: Successfully determining competitive optimal schedules for electricity generation intimately hinges on the forecasts of loads. The nonstationarity and high volatility of loads make their accurate prediction somewhat problematic. Presence of uncertainty in data also significantly degrades accuracy of point predictions produced by deterministic load forecasting models. Therefore, operation planning utilizing these predictions will be unreliable. This paper aims at developing prediction intervals rather than producing exact point prediction. Prediction intervals are theatrically more reliable and practical than predicted values. The delta and Bayesian techniques for constructing prediction intervals for forecasted loads are implemented here. To objectively and comprehensively assess quality of constructed prediction intervals, a new index based on length and coverage probability of prediction intervals is developed. In experiments with real data, and through calculation of global statistics, it is shown that neural network point prediction performance is unreliable. In contrast, prediction intervals developed using the delta and Bayesian techniques are satisfactorily narrow, with a high coverage probability.