Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Abstract

SummaryAdaptive cluster sampling is an efficient method of estimating the parameters of rare and clustered populations. The method mimics how biologists would like to collect data in the field by targeting survey effort to localised areas where the rare population occurs. Another popular sampling design is inverse sampling. Inverse sampling was developed so as to be able to obtain a sample of rare events having a predetermined size. Ideally, in inverse sampling, the resultant sample set will be sufficiently large to ensure reliable estimation of population parameters. In an effort to combine the good properties of these two designs, adaptive cluster sampling and inverse sampling, we introduce inverse adaptive cluster sampling with unequal selection probabilities. We develop an unbiased estimator of the population total that is applicable to data obtained from such designs. We also develop numerical approximations to this estimator. The efficiency of the estimators that we introduce is investigated through simulation studies based on two real populations: crabs in Al Khor, Qatar and arsenic pollution in Kurdistan, Iran. The simulation results show that our estimators are efficient.

Adaptive two-stage inverse sampling design to estimate density, abundance, and occupancy of rare and clustered populations

“…Aggarwaland and Pandey [ 6 ] used inverse sampling to study disease burden of leprosy in an endemic area of Uttar Pradesh, India. Salehi et al [ 7 ] introduced inverse adaptive cluster sampling with unequal selection probabilities to study crab holes. Panahbehagh and Smith [ 8 ] developed group inverse sampling which is practical for field implementation.…”

A proposal for a two-step sampling design to oversample units responding to prescribed characteristics

“…and applied in a variety of instances in the environmental field ( [29], [22], [26], [9]). Adaptive sampling is characterized by the fact that the procedure used to select units depends on evidence collected during the survey itself; a notable feature of adaptive designs is that they are typically well suited to surveying populations where the variable of interest has a highly skewed distribution, also in a geographical sense ( [28], [27], [20]); for example, when dealing with a dichotomous survey variable such as the presence or absence of a rare and geographically clustered characteristic, adaptive sampling strategies have proved to be reliable in over-representing units that have the trait of interest, while retaining the possibility of drawing valid inference [1]. Over-representation of units responding to prescribed characteristics may be a highly desirable feature, especially when resources are limited: in the environmental setting, budget constraints usually limit the possible survey effort ( [11]), hence emphasising the need for an efficient use of the available resources.…”