The double sampling method known as “big BAF sampling” has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce’s method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce’s method is not known to most foresters who use the method in practice. We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

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关于大BAF采样方差估计的注释

提倡使用称为“大BAF采样”的双重采样方法，以减少采样工作，同时仍保持合理准确的体积估计。通常使用一种众所周知的方差确定方法，布鲁斯方法，因为体积估算器采用随机变量乘积的形式。但是，对于大多数在实践中使用该方法的林务员来说，布鲁斯方法的起源尚不清楚。我们确定泰勒级数逼近被称为Delta方法，为Bruce方法的起源提供了合理的解释。在两个不同的树种群上进行了仿真，以确定Delta方法与产品的确切方差的相似性。此外，还有两个替代估算器，用于估算单个树的体积-基础面积比的方差，在整体方差估算程序中对估算过程的一部分进行了比较。仿真结果表明，布鲁斯方法为估计采用大BAF方法进行的库存差异提供了一种鲁棒的方法。该模拟还表明，可以使用均值的常规样本方差或具有相等精度的比率方差估计量来计算平均体积-面积比的方差，而以前在大BAF采样中没有显示过。布鲁斯方法的起源的合理解释已经在历史上和数学上在三角洲方法中提出。在大多数情况下，应用产品的确切方差或Delta方法显然没有实际区别-均可使用。