
A New Confidence Interval for the Mean of a Bounded Random Variable
We present a new method for constructing a confidence interval for the m...
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Empirical Decision Rules for Improving the Uncertainty Reporting of Small Sample System Usability Scale Scores
The System Usability Scale (SUS) is a short, surveybased approach used ...
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On the lengths of tbased confidence intervals
Given n=mk iid samples from N(θ,σ^2) with θ and σ^2 unknown, we have two...
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Optimal Mean Estimation without a Variance
We study the problem of heavytailed mean estimation in settings where t...
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Parametric Bootstrap Confidence Intervals for the Multivariate FayHerriot Model
The multivariate FayHerriot model is quite effective in combining infor...
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Discussion of "On nearly assumptionfree tests of nominal confidence interval coverage for causal parameters estimated by machine learning"
We congratulate the authors on their exciting paper, which introduces a ...
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Towards Practical Mean Bounds for Small Samples
Historically, to bound the mean for small sample sizes, practitioners ha...
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Error analysis for smallsample, highvariance data: Cautions for bootstrapping and Bayesian bootstrapping
Recent advances in molecular simulations allow the direct evaluation of kinetic parameters such as rate constants for protein folding or unfolding. However, these calculations are usually computationally expensive and even significant computing resources may result in a small number of independent rate estimates spread over many orders of magnitude. Such small, highvariance samples are not readily amenable to analysis using the standard uncertainty ("standard error of the mean") because unphysical negative limits of confidence intervals result. Bootstrapping, a natural alternative guaranteed to yield a confidence interval within the minimum and maximum values, also exhibits a striking systematic bias of the lower confidence limit. As we show, bootstrapping artifactually assigns high probability to improbably low mean values. A second alternative, the Bayesian bootstrap strategy, does not suffer from the same deficit and is more logically consistent with the type of confidence interval desired, but must be used with caution nevertheless. Neither standard nor Bayesian bootstrapping can overcome the intrinsic challenge of underestimating the mean from small, highvariance samples. Our report is based on extensive reanalysis of multiple estimates for rate constants obtained from independent atomistic simulations. Although we only analyze rate constants, similar considerations may apply to other types of highvariance calculations, such as may occur in highly nonlinear averages like the Jarzynski relation.
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