Constructing Orthogonal Replications for Variance Estimation

Gurney, Margaret; Jewett, Robert S.

doi:10.2307/2285442

Cited by 5 publications

(4 citation statements)

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“…The variance estimate (eq 9) is similar to that used in the method of balanced repeated replications 69,70 for estimating the variance of a nonlinear statistic in stratified random sampling, where orthogonal replications are employed instead of random replications as above. Note that the variance estimate of ΔF ̂could be S/4, because the variance of ΔF ̂(j 1 , ..., j M ) is that of ΔF ̂multiplied by 4 according to different sample sizes.…”

Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix

Cui

Zhang

Tan

et al. 2019

J. Chem. Theory Comput.

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Free energy perturbation (FEP) simulations have been widely applied to obtain predictions of the relative binding free energy for a series of congeneric ligands binding to the same receptor, which is an essential component for the lead optimization process in computer-aided drug discovery. In the case of several congeneric ligands forming a perturbation map involving a closed thermodynamic cycle, the summation of the estimated free energy change along each edge in the cycle using BAR (Bennett acceptance ratio) usually will deviate from zero due to systematic and random errors, which is the hysteresis of cycle closure. In this work, the advanced reweighting techniques UWHAM (binless weighted histogram analysis method) and LWHAM (locally weighted histogram analysis method) are applied to provide statistical estimators of the free energy change along each edge in order to eliminate the hysteresis effect. As an example, we analyze a closed thermodynamic cycle involving four congeneric ligands which bind to HIV-1 integrase, a promising target which has emerged for antiviral therapy. We demonstrate that compared with FEP and BAR, more accurate and hysteresis-free estimates of free energy differences can be achieved by using UWHAM to find a single estimate of the density of states based on all of the data in the cycle. Furthermore, by comparison of LWHAM results obtained from the inclusion of different numbers of neighboring states with UWHAM estimation involving all the states, we show how to determine the optimal neighborhood size in the LWHAM analysis to balance the tradeoffs between computational cost and accuracy of the free energy prediction. Even with the smallest neighborhood, LWHAM can improve the BAR free energy estimates using the same input data as BAR. We introduce an overlapping states matrix that is constructed by using the global jump formula of LWHAM and plot its heat map. The heat map provides a quantitative measure of the overlap between pairs of alchemical/thermodynamic states. We explain how to identify and improve the FEP calculations along the edges that most likely cause large systematic errors by using the heat map of the overlapping states matrix and by comparing the BAR and UWHAM estimates of the free energy change.

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Section: Journal Of Chemical Theory and Computationmentioning

confidence: 99%

Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix

Cui

Zhang

Tan

et al. 2019

J. Chem. Theory Comput.

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“…Generalizations of BRR to designs with more than two PSUs per stratum have been proposed (Gurney and Jewett 1975;Gupta and Nigam 1987;Wu 1991;Sitter 1993) but did not find widespread use in practice because of excessive mathematical complexity and limited availability of the orthogonal arrays necessary to construct the BRR schemes.…”

Section: Survey: Logistic Regressionmentioning

confidence: 99%

Resampling Variance Estimation for Complex Survey Data

Kolenikov

2010

The Stata Journal: Promoting communications on statistics and S

148

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In this article, I discuss the main approaches to resampling variance estimation in complex survey data: balanced repeated replication, the jackknife, and the bootstrap. Balanced repeated replication and the jackknife are implemented in the Stata svy suite. The bootstrap for complex survey data is implemented by the bsweights command. I describe this command and provide working examples. Editors' note. This article was submitted and accepted before the new svy bootstrap prefix was made available in the Stata 11.1 update. The variance estimation method implemented in the new svy bootstrap prefix is equivalent to the one in bs4rw. The only real difference is syntax. For example,. bs4rw, rw(bw*): logistic highbp height weight age female [pw=finalwgt] is equivalent to. svyset [pw=finalwgt], vce(bootstrap) bsrweight(bw*). svy: logistic highbp height weight age female Similarly, the example using mean bootstrap replicate weights,. local mean2fay = 1-sqrt(1/10). svyset [pw=finalwgt], vce(brr) brrweight(bw*) fay(`mean2fay´). svy: logistic highbp height weight age female is equivalent to. svyset [pw=finalwgt], vce(bootstrap) bsrweight(bw*) bsn(10). svy: logistic highbp height weight age female The weights created by the bsweights command discussed in this article are equally applicable with the bs4rw command and with the new vce(bootstrap) and bsrweight() options of svy and svyset.

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“…Obviously, we desire a k large enough to provide a reasonable estimate, small enough to be tractable, and sufficient for balancing. Both Wolter [11] and Gurney & Jewett [13] suggest a construction originally from [18]: use p β replicates where β satisfies the inequality L¨¤ 2 β¨1 To the best of the authors' knowledge, [14] is the earliest work to discuss, in detail, the use of BRR for the application of confidence intervals. Frankel states that "the distribution of the ratio of the first-order sample estimate minus its expected value, to its estimated standard error is reasonably approximated by Student's-t within symmetric intervals."…”

Section: Balanced Half-samplingmentioning

confidence: 99%

“…As shown in [13] and [11], the BRR paradigm can be extended to any case where the PSU is prime. We do not present this case here, since there is limited space and it does not provide any additional intuition for the reader.…”

Section: Balanced Half-samplingmentioning

confidence: 99%