Statistical Uncertainty Analysis for Small-Sample, High Log-Variance Data: Cautions for Bootstrapping and Bayesian Bootstrapping

被引:18
|
作者
Mostofian, Barmak [1 ]
Zuckerman, Daniel M. [1 ]
机构
[1] Oregon Hlth & Sci Univ, Sch Med, Dept Biomed Engn, Portland, OR 97239 USA
关键词
MOLECULAR-DYNAMICS SIMULATIONS; WEIGHTED ENSEMBLE SIMULATION; PROTEIN; KINETICS;
D O I
10.1021/acs.jctc.9b00015
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive, and even significant computing resources may result in a small number of independent estimates spread over many orders of magnitude. Such small-sample, high "log-variance" data are not readily amenable to analysis using the standard uncertainty (i.e., "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 in log space. 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. The Bayesian bootstrap provides uncertainty intervals that are more reliable than those from the standard bootstrap method but must be used with caution nevertheless. Neither standard nor Bayesian bootstrapping can overcome the intrinsic challenge of underestimating the mean from small-size, high log-variance samples. Our conclusions are based on extensive analysis of model distributions and reanalysis of multiple independent atomistic simulations. Although we only analyze rate constants, similar considerations will apply to related calculations, potentially including highly nonlinear averages like the Jarzynski relation.
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页码:3499 / 3509
页数:11
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