Statistical techniques for sampling and monitoring natural resources

Abstract

We present the statistical theory of inventory and monitoring from a probabilistic point of view. We start with the basics and show the interrelationships between designs and estimators illustrating the methods with a small artificial population as well as with a mapped realistic population. For such applications, useful open source software is given in Appendix 4. Various sources of ancillary information are described and applications of the sampling strategies are discussed. Classical and bootstrap variance estimators are discussed also. Numerous problems with solutions are given, often based on the experiences of the authors. Key additional references are cited as needed or desired. Problem: Two random samples of size n are taken without replacement from a population. By pure chance, the two samples are identical. Are the 2 estimates independent? Answer: Yes, they are. Problem. In the above example, how would you go about combining the two samples? Answer. The most sensible solution would probably be to treat it as a sample of size 2n with replacement even though each sample in itself was taken without replacement. The advantage of this is that the variance estimate would typically be an overestimate of the actual variance.

Spatial upscaling using thematic maps: An analysis of uncertainties in permafrost soil carbon estimates

“…[16] When the variance of a statistical population can be estimated, the sample size n needed to detect a given precision (P) with a 1-a probability can be calculated using the formula [Schreuder et al, 2004]:…”

Remote Sensing Based Two-Stage Sampling for Accuracy Assessment and Area Estimation of Land Cover Changes

“…Approximate equations for the associated accuracy statistics and standard errors are usually given in such cases, e.g., in [21,23]. Instead of applying such approximate and highly complex equations, which are often based on normal distribution assumptions, the current approach uses bootstrapping, as confidence intervals can be constructed without having to make normal theory assumptions [18]. The main drawback of the current approach lies in the added complexity for stratification within the cluster sampling design.…”

“…For example, the 95% confidence interval has a 95% probability of enclosing the true value. In the proposed approach, bootstrapping is applied for derivation of the confidence intervals as, e.g., described in [18,19], where the selection of the bootstrap samples emulates the actual sample selection method. Bootstrapping is thus performed by repeated sampling of the PSUs and SSUs from the whole sample set with replacement.…”

Statistics and quality assurance for the Northern Research Station Forest Inventory and Analysis Program, 2016

“…FIA inventories are commonly designed to meet the specified sampling errors at the state level at the 68 percent confidence limit (one standard error). See Schreuder et al (2004) for the derivation of standard error of a population. The "Forest Survey Handbook" mandates that the sampling error for area cannot exceed 3 percent per 1 million acres of timberland.…”

“…Schreuder et al (2004) serves as a complete introduction to the statistical techniques of sampling natural resources starting at a very basic level and progressing to more advanced methods. The book includes introductory material, much of which is taken from the excellent introductory book by Freese (1962).…”