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Coverage probability

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


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Proceedings ArticleDOI
10 Dec 2000
TL;DR: Applying ABATCH, ASAP, and LBATCH to the analysis of a suite of twenty test problems involving discrete-time Markov chains, time-series processes, and queueing systems, it is found ASAP to deliver confidence intervals that not only satisfy a user-specified absolute or relative precision requirement but also frequently outperform the corresponding confidence intervals delivered by ABATCH andLBATCH.
Abstract: We summarize the results of an extensive experimental performance evaluation of selected batch means procedures for building a confidence interval for a steady-state expected simulation response. We compare the performance of the well-known ABATCH and LBATCH procedures versus ASAP, a recently proposed variant of the method of nonoverlapping batch means (NOBM) that operates as follows: the batch size is progressively increased until either (a) the batch means pass the von Neumann test for independence, and then ASAP delivers a classical NOBM confidence interval; or (b) the batch means pass the Shapiro-Wilk test for multivariate normality, and then ASAP delivers a correlation-adjusted confidence interval. The latter correction is based on an inverted Cornish-Fisher expansion for the classical NOBM t-ratio, where the terms of the expansion are estimated via an autoregressive-moving average time series model of the batch means. Applying ABATCH, ASAP, and LBATCH to the analysis of a suite of twenty test problems involving discrete-time Markov chains, time-series processes, and queueing systems, we found ASAP to deliver confidence intervals that not only satisfy a user-specified absolute or relative precision requirement but also frequently outperform the corresponding confidence intervals delivered by ABATCH and LBATCH with respect to coverage probability.

24 citations

Journal ArticleDOI
TL;DR: Assuming that some extreme sample values have been censored or discarded, a reliability analysis of several two-parameter models, as the exponential, Pareto and power-function laws, is presented.

24 citations

Journal ArticleDOI
TL;DR: In this paper, the authors advocate the use of Formulas (4.1) and 4.2) in providing interval forecasts, arguing that these formulas require many strong assumptions including that the underlying model is the true model, the innovational distribution is normal, and the forecasts are unbiased.
Abstract: I am not surprised by how far behind our profession is in calculating interval forecasts. After all, interval forecast is a concept not well formulated nor well understood by statisticians. On the other hand, I am amazed by Chatfield's expectation and his recommendation. Will he be satisfied when Formulas (4.1) and (4.2) are routinely used in practice? Will he be satisfied when the forecast intervals are sufficiently wide to cover all the data points in out-of-sample forecasts? I agree totally that point forecasts fail to provide uncertainty assessment of the future, and some assessment on uncertainty must be given in prediction. Are interval forecasts the solution to uncertainty assessment, however? In particular, I am unhappy about advocating the routine use of Formulas (4.1) and (4.2) in providing interval forecasts. First of all, the formulas require many strong assumptions including that (a) the underlying model is the "true" model, (b) the innovational distribution is normal, and (c) the forecasts are unbiased. Since these assumptions are always violated in practice, what can a practitioner do? Second, the probability statement associated with an interval forecast tends to be misleading. The actual coverage probability is often different from the stated probability coefficient. Is there not a danger that we might provide a false impression on the accuracy in probability statement when we give a 95% prediction interval (PI) based on these formulas? Third, judging a PI by its length is misleading. For a reasonable PI, the coverage probability is more relevant. Considering the example of Section 7, I can see the value of increasing the upper bound from 8.73 to 11.14 for the 12-step-ahead PI. I would regard lowering the lower bound from 2.66 to .86 as a disservice, however. Does Chatfield believe the U.S. quarterly unemployment rate is ever lower than 2.0? In this particular instance, widening the PI by lowering the lower bound, resulting from the mechanical use of formulas (4.1) and (4.2), seems questionable. At least, it is in conflict with common sense.

24 citations

Journal ArticleDOI
TL;DR: Experimental results demonstrate that the LASSO-QR method can construct more accurate PI and obtain more precise probability density forecasting results than quantile regression (QR).

24 citations

Posted Content
TL;DR: In this paper, the authors propose relative magnitude and relative standard deviation stopping rules in the context of Markov chain Monte Carlo (MCMC) simulations for estimating features of a target distribution, particularly for Bayesian inference.
Abstract: Markov chain Monte Carlo (MCMC) simulations are commonly employed for estimating features of a target distribution, particularly for Bayesian inference. A fundamental challenge is determining when these simulations should stop. We consider a sequential stopping rule that terminates the simulation when the width of a confidence interval is sufficiently small relative to the size of the target parameter. Specifically, we propose relative magnitude and relative standard deviation stopping rules in the context of MCMC. In each setting, we develop sufficient conditions for asymptotic validity, that is conditions to ensure the simulation will terminate with probability one and the resulting confidence intervals will have the proper coverage probability. Our results are applicable in a wide variety of MCMC estimation settings, such as expectation, quantile, or simultaneous multivariate estimation. Finally, we investigate the finite sample properties through a variety of examples and provide some recommendations to practitioners.

24 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202363
2022153
2021142
2020151
2019142