Back to Search Start Over

A note on the estimation of variance for big BAF sampling

Authors :
Jeffrey H. Gove
Timothy G. Gregoire
Mark J. Ducey
Thomas B. Lynch
Source :
Forest Ecosystems, Vol 7, Iss 1, Pp 1-14 (2020)
Publication Year :
2020
Publisher :
KeAi Communications Co., Ltd., 2020.

Abstract

Abstract Background 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. Methods 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. Results 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. Conclusions 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.

Details

Language :
English
ISSN :
21975620
Volume :
7
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Forest Ecosystems
Publication Type :
Academic Journal
Accession number :
edsdoj.53161048e8224d79941dc5a386fca0e6
Document Type :
article
Full Text :
https://doi.org/10.1186/s40663-020-00272-x