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This paper develops a general central limit theorem (CLT) for post-stratified Monte Carlo estimators with an associated infinite number of strata. In addition, consistency of the corresponding variance estimator is established in the same setting. With these results in hand, one can then construct asymptotically valid confidence interval procedures for such infinitely stratified estimators. We then illustrate our general theory, by applying it to the specific case of debiased multi-level Monte Carlo (MLMC) algorithms. This leads to the first asymptotically valid confidence interval procedure for such stratified debiased MLMC procedures. [ABSTRACT FROM AUTHOR]

Joinpoint regression analysis was applied to calculate the average annual percent change (AAPC), with 95% confidence interval (CI), to evaluate global ischemic heart disease (IHD) mortality trends in 1990–2019. In 2019, there were disparities by sex in terms of the contribution of non-optimal temperature to global IHD mortality: for low temperature (5.99% in males and 6.19% in females, respectively) and high temperature (0.50% in males and 0.44% in females, respectively). A decreasing trend for global IHD mortality attributed to low temperature was observed in males (AAPC = −1.7%; 95% CI = −1.8 to −1.6) and females (AAPC = −2.1%; 95% CI = −2.1 to −2.0). [ABSTRACT FROM AUTHOR]

Neutron detection systems utilize statistical alarm techniques where a measured false alarm rate (FAR) can vary drastically from the FAR predicted by a theoretical model. The ability to set an alarm threshold that results in a practically controlled FAR is crucial to characterize detector sensitivity with both accuracy and precision. A generalized and automated method is presented to statistically evaluate FAR performance by assuming that the FAR itself is not deterministic, but a normal stochastic process over a specific parameter to be corrected that will hereafter be referred to as the correction. In this manner, a specific correction results in not only a point estimate of FAR, but also a confidence interval. The central objective is focused exclusively on characterization assuming that experiments are executed in a tightly controlled environment so that an accurate comparison is enabled across detectors. Once a correction is calculated, the estimated FAR is only assumed accurate in a similar environment for sensitivity evaluation. Initially, the calculated correction factor was used to compare FARs across various distributions including normal, corrected normal, Poisson, and a simplified normal distribution. Later verification data sets were used to empirically demonstrate the rate of containment of measured confidence coefficients using two detectors of different technology. A second application uses the correction method to improve the signal-to-noise ratio metric to agree more with dynamic sensitivity results. Finally, a third application studies the effect of altering the duration of background acquisition on FAR performance. [ABSTRACT FROM AUTHOR]