Adaptive Simple Random Sampling
Also known as: ASRS, adaptive SRS, adaptive random sampling, sequential adaptive sampling
Adaptive simple random sampling (ASRS) begins with a conventional simple random sample and then expands the sample in regions where the variable of interest exceeds a pre-specified threshold. Units neighboring a qualifying observation are added to the sample, allowing the design to concentrate effort where the population is dense or rare, while retaining unbiased estimation through the Horvitz-Thompson or Hansen-Hurwitz estimators. The approach was systematized by Steven K. Thompson in the early 1990s as part of the broader adaptive sampling framework.
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When to use it
Use adaptive simple random sampling when the variable of interest is rare, clustered, or both — for example, rare plant populations, wildlife colonies, disease hot spots, or illicit crop patches. The method pays off when an initial SRS would encounter many empty or zero-valued units, wasting survey effort. ASRS is particularly well-suited to spatial ecological surveys, environmental monitoring, and epidemiological fieldwork where the distribution of cases is highly uneven. Do not use it when the population is uniformly distributed or the variable has no spatial autocorrelation, as the adaptive expansion will rarely trigger and the added design complexity yields no efficiency gain over plain SRS. It is also poorly suited to surveys where revisiting or adding units mid-survey is logistically costly, or where the threshold criterion cannot be specified meaningfully before data collection.
Strengths & limitations
- Concentrates sample effort in areas of high density or rare occurrence, substantially reducing variance compared to plain SRS when the population is clustered.
- Retains full probability-sampling properties: the Horvitz-Thompson estimator is unbiased regardless of where the adaptive expansion leads.
- Flexible adjacency definition allows the design to be tailored to domain-specific proximity concepts (grid neighbors, geographic buffers, network links).
- Increases the probability of detecting rare phenomena without requiring prior knowledge of their exact locations.
- Compatible with stratified or multistage designs at the first-phase level, making it embeddable in complex survey architectures.
- Final sample size is random and unpredictable, which complicates budgeting and field logistics.
- Efficiency gains are realized only when the target variable is genuinely clustered; for uniform populations ASRS offers no advantage over SRS.
- The adaptive criterion c must be fixed before data collection; a poorly chosen threshold can result in excessive or negligible expansion.
- Horvitz-Thompson estimation requires knowledge of network inclusion probabilities, which can be complex to compute for irregular network structures.
- Analysis is more computationally demanding than standard SRS; specialized software or custom code is typically required.
Frequently asked
How is adaptive simple random sampling different from adaptive cluster sampling?
Adaptive cluster sampling (ACS) is the most studied variant in the adaptive sampling family and is sometimes used as a synonym for the general framework. Strictly speaking, ACS refers to any adaptive design with a clustering expansion rule, while adaptive simple random sampling specifies that the initial sample is drawn by SRS. In Thompson's formulation, adaptive simple random sampling is the canonical version of ACS where the first-phase design is a simple random sample without replacement.
Is the Horvitz-Thompson estimator really unbiased under adaptive expansion?
Yes, provided the threshold criterion is fixed before sampling begins and the adjacency rule is applied consistently. The unbiasedness follows from the fact that every unit in the population has a calculable — though not equal — probability of being included in the final sample, allowing the Horvitz-Thompson weights to correct for differential selection. The critical requirement is that the adaptive rule cannot be modified in response to incoming data.
How do I choose the threshold c?
The threshold should be chosen based on subject-matter knowledge before data collection — for example, a count above which a unit is considered 'occupied' by the rare species of interest. Simulation studies or pilot data can help evaluate how different values of c affect the expected sample size and variance. A low c triggers frequent expansion and a larger, more variable sample size; a high c limits expansion and reduces efficiency gains.
What software can I use for adaptive simple random sampling?
The R packages 'ACSampling' and 'SDraw' provide functions for designing and analysing adaptive cluster samples. Custom implementation in R or Python is also common, particularly for irregular grids or non-standard adjacency structures. Standard survey software (e.g., SAS PROC SURVEYMEANS, Stata svy commands) does not natively support adaptive designs and should not be used without modification.
When does ASRS perform worse than plain SRS?
When the target variable is uniformly distributed across the population, the adaptive criterion is rarely triggered, expansion is minimal, and the additional complexity of the design yields no variance reduction. In such cases plain SRS is simpler, cheaper, and equally efficient. ASRS is also less competitive when the population is large relative to the cluster size, because the inclusion probabilities of network units become very small and the Horvitz-Thompson estimator can have high variance.
Sources
- Thompson, S. K. (1992). Sampling. John Wiley & Sons. ISBN: 978-0471548850
- Thompson, S. K., & Seber, G. A. F. (1996). Adaptive Sampling. John Wiley & Sons. ISBN: 978-0471558712
How to cite this page
ScholarGate. (2026, June 3). Adaptive Simple Random Sampling. ScholarGate. https://scholargate.app/en/survey-methodology/adaptive-simple-random-sampling
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Adaptive Cluster SamplingSurvey Methodology↔ compare
- Multistage SamplingSurvey Methodology↔ compare
- Simple random samplingSurvey Methodology↔ compare
- Stratified SamplingSurvey Methodology↔ compare
- Systematic SamplingSurvey Methodology↔ compare