Adaptive Sampling Designs Research Articles

Adaptive cluster sampling for negatively correlated data

Adaptive cluster sampling is a design specifically developed for rare and clustered populations. Using this sampling design, we consider the case when an auxiliary variable is available in addition to the variable of interest. The use of auxiliary information has been shown to improve the efficiency of estimators although this results in asymptotically design‐unbiased estimators. Consider wildlife population in a protected area. Its distribution and abundance can partly be influenced by such factors as disease and pollution where the presence of wildlife diseases or higher environmental pollution decreases population totals and the distribution of wildlife. This paper proposes two product estimators and their associated variance estimators for the adaptive cluster sampling design to be used when the study and auxiliary variables are negatively correlated. The exact expression of the bias together with the mean square error to the first degree of approximation has been obtained. We derived the conditions under which the proposed estimators provided a more accurate estimation than the Horvitz–Thompson and Hansen–Hurwitz estimators with adaptive cluster sampling and the product estimator with simple random sampling. A simulation study was carried out to show the performance of the proposed estimators. Moreover, theoretical findings were supported by a numerical example using real data. Copyright © 2016 John Wiley & Sons, Ltd.

Temporally adaptive sampling: a case study in rare species survey design with marbled salamanders (Ambystoma opacum).

Improving detection rates for elusive species with clumped distributions is often accomplished through adaptive sampling designs. This approach can be extended to include species with temporally variable detection probabilities. By concentrating survey effort in years when the focal species are most abundant or visible, overall detection rates can be improved. This requires either long-term monitoring at a few locations where the species are known to occur or models capable of predicting population trends using climatic and demographic data. For marbled salamanders (Ambystoma opacum) in Massachusetts, we demonstrate that annual variation in detection probability of larvae is regionally correlated. In our data, the difference in survey success between years was far more important than the difference among the three survey methods we employed: diurnal surveys, nocturnal surveys, and dipnet surveys. Based on these data, we simulate future surveys to locate unknown populations under a temporally adaptive sampling framework. In the simulations, when pond dynamics are correlated over the focal region, the temporally adaptive design improved mean survey success by as much as 26% over a non-adaptive sampling design. Employing a temporally adaptive strategy costs very little, is simple, and has the potential to substantially improve the efficient use of scarce conservation funds.

Efficiency of the Adaptive Cluster Sampling Designs in Estimation of Rare Populations

Adaptive cluster sampling (ACS) has been a very important tool in estimation of population parameters of rare and clustered population. The fundamental idea behind this sampling plan is to decide on an initial sample from a defined population and to keep on sampling within the vicinity of the units that satisfy the condition that at least one characteristic of interest exists in a unit selected in the initial sample. Despite being an important tool for sampling rare and clustered population, adaptive cluster sampling design is unable to control the final sample size when no prior knowledge of the population is available. Thus adaptive cluster sampling with data-driven stopping rule (ACS’) was proposed to control the final sample size when prior knowledge of population structure is not available. This study examined the behavior of the HT, and HH estimator under the ACS design and ACS’ design using artificial population that is designed to have all the characteristics of a rare and clustered population. The efficiencies of the HT and HH estimator were used to determine the most efficient design in estimation of population mean in rare and clustered population. Results of both the simulated data and the real data show that the adaptive cluster sampling with stopping rule is more efficient for estimation of rare and clustered population than ordinary adaptive cluster sampling.

A comparison of adaptive sampling designs and binary spatial models : a simulation study using a census of Bromus inermis

Commonly in environmental and ecological studies, species distribution data are recorded as presence or absence throughout a spatial domain of interest. Field based studies typically collect observations by sampling a subset of the spatial domain. We consider the effects of six different adaptive and two non‐adaptive sampling designs and choice of three binary models on both predictions to unsampled locations and parameter estimation of the regression coefficients (species–environment relationships). Our simulation study is unique compared to others to date in that we virtually sample a true known spatial distribution of a nonindigenous plant species, Bromus inermis. The census of B. inermis provides a good example of a species distribution that is both sparsely (1.9 % prevalence) and patchily distributed. We find that modeling the spatial correlation using a random effect with an intrinsic Gaussian conditionally autoregressive prior distribution was equivalent or superior to Bayesian autologistic regression in terms of predicting to un‐sampled areas when strip adaptive cluster sampling was used to survey B. inermis. However, inferences about the relationships between B. inermis presence and environmental predictors differed between the two spatial binary models. The strip adaptive cluster designs we investigate provided a significant advantage in terms of Markov chain Monte Carlo chain convergence when trying to model a sparsely distributed species across a large area. In general, there was little difference in the choice of neighborhood, although the adaptive king was preferred when transects were randomly placed throughout the spatial domain. Copyright © 2013 John Wiley & Sons, Ltd.

Bootstrap confidence intervals for adaptive cluster sampling design based on Horvitz–Thompson type estimators

Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) introduced several bootstrap methods under adaptive cluster sampling using a Horvitz–Thompson type estimator. Using a simulation study, they showed that their proposed methods provide confidence intervals with highly understated coverage rates. In this article, we first show that their bootstrap methods provide biased bootstrap estimates. We then define two bootstrap methods, based on the method of Gross (Proceeding of the survey research methods section. American Statistical Association, Alexandria, VA, pp 181–184, 1980) and Bootstrap With Replacement, that provide unbiased bootstrap estimates of the population mean with bootstrap variances matching the corresponding unbiased variance estimator. Using a simulation study, we show that the bootstrap confidence intervals based on our proposed methods have better performance than those based on available bootstrap methods, in the sense of having coverage proportion closer to the nominal coverage level. We also compare the proposed intervals to empirical likelihood based intervals in small samples.

An approximation method to calculate complicated expectations

In some adaptive sampling designs, expectations need to be calculated as sampling progresses. For situations when these calculations need to be done in the field where there is no acce ss to computers, or for very complicated and computer intensive calculations, we introduce an approximation method. The method to approximate the expectation is based on conditioning on small set of points. An application of the approximation method is described for a sample design with a complicated estimator.

Regression-type estimators for adaptive two-stage sequential sampling

Adaptive two-stage sequential sampling (ATSSS) design was developed to observe more rare units and gain higher efficiency, in the sense of having a smaller variance estimator, than conventional sampling designs with equal effort for rare and spatially cluster populations. For certain rare populations, incorporating auxiliary variables into a sampling design can further improve the observation of rare units and increase efficiency. In this article, we develop regression-type estimators for ATSSS so that auxiliary variables can be incorporated into the ATSSS design when warranted. Simulation studies on two populations show that the regression-type estimators can significantly increase the efficiency of ATSSS and the detection of more rare units as compared to conventional sampling counterparts. Simulation of sampling of desert shrubs in Inner Mongolia (one of the two populations studied) showed that by incorporating a GIS auxiliary variable into ATSSS with the regression estimators resulted in a gain in efficiency over ATSSS without the auxiliary variable. Further, we found that the use of the GIS auxiliary variable in a conventional two-stage design with a regression estimator did not show a gain in efficiency.

The impact of remittances and equivalence scales on poverty in Tajikistan

The aim of this paper is to study the impact of remittances from labour migrants on welfare, as well as the impact of the use of equivalence scales on poverty, in Tajikistan. The magnitude of remittances sent back is fairly well known from official statistics (e.g. the amount of remittances is regularly monitored by the balance of payment at the Central Bank). In 2009 a change in the flow of money from abroad occurred, and volumes dropped, but it was unknown to what extent; its impact on poverty is still officially unknown. This paper describes a project aimed at conducting a survey to investigate this impact. It would not be possible to do this kind of analysis with a traditional sample survey, since it would generate only a small selection of migrant households. Instead, the new Migration, Remittances and Poverty Survey was used, which was conducted by the Tajik State Statistical Office in August 2010 using an adaptive sampling design from a set of enumeration areas selected mainly from the 2009 Integrated Household Budget Survey (IHBS) and showing households with remittances. To evaluate the impact of equivalence scales on poverty measures, new scales have been estimated on the basis of consumption expenditure from the 2009 IHBS.

Adaptive web sampling in ecology

Adaptive sampling strategies for ecological and environmental studies are described in this paper. The motivations for adaptive sampling are discussed. Developments in this area over recent decades are reviewed. Adaptive cluster sampling and a number of its variations are described. The newer class of adaptive web sampling designs and their spatial sampling uses are discussed. Case studies in the use of adaptive sampling strategies with ecological populations are cited. The nature of optimal sampling strategies is described. Design-based and model-based approaches to inference with adaptive sampling strategies are summarized.

Adaptive Cluster Sampling in the Context of Restoration

AbstractAbundance is an important population state variable for monitoring restoration progress. Efficient sampling often proves difficult, however, when populations are sparse and patchily distributed, such as early after restoration planting. Adaptive cluster sampling (ACS) can help by concentrating search effort in high density areas, improving the encounter rate and the ability to detect a population change over time. To illustrate the problem, I determined conventional design sample sizes for estimating abundance of 12 natural populations and 24 recently planted populations (divided among two preserves) of Lupinus perennis L. (wild blue lupine). I then determined the variance efficiency of ACS relative to simple random sampling at fixed effort and cost for 10 additional planted populations in two habitats (field vs. shrubland). Conventional design sample sizes to estimate lupine stem density with 10% or 20% margins of error were many times greater than initial sample size and would require sampling at least 90% of the study area. Differences in effort requirements were negligible for the two preserves and natural versus planted populations. At fixed sample size, ACS equaled or outperformed simple random sampling in 40% of populations; this shifted to 50% after correcting for travel time among sample units. ACS appeared to be a better strategy for inter‐seeded shrubland habitat than for planted field habitat. Restoration monitoring programs should consider adaptive sampling designs, especially when reliable abundance estimation under conventional designs proves elusive.

Adaptive survey designs for sampling rare and clustered populations

Designing an efficient large-area survey is a challenge, especially in environmental science when many populations are rare and clustered. Adaptive and unequal probability sampling designs are appealing when populations are rare and clustered because survey effort can be targeted to subareas of high interest. For example, higher density subareas are usually of more interest than lower density areas. Adaptive and unequal probability sampling offer flexibility for designing a long-term survey because they can accommodate changes in survey objectives, changes in underlying environmental habitat, and changes in species-habitat models. There are many different adaptive sampling designs including adaptive cluster sampling, two-phase stratified sampling, two-stage sequential sampling, and complete allocation stratified sampling. Sample efficiency of these designs can be very high compared with simple random sampling. Large gains in efficiency can be made when survey effort is targeted to the subareas of the study site where there are clusters of individuals from the underlying population. These survey methods work by partitioning the study area in some way, into strata, or primary sample units, or in the case of adaptive cluster sampling, into networks. Survey effort is then adaptively allocated to the strata or primary unit where there is some indication of higher species counts. Having smaller, and more numerous, strata improves efficiency because it allows more effective targeting of the adaptive, second-phase survey effort.

Efficiency of Two-Stage Adaptive Cluster Sampling Design in Estimating Fringe-Eared Oryx

Two-stage adaptive cluster sampling and two-stage conventional sampling designs were used to estimate population total of Fringe-Eared Oryx that are clustered and sparsely distributed. The study region was Amboseli-West Kilimanjaro and Magadi-Natron cross boarder landscape between Kenya and Tanzania. The study region was partitioned into different primary sampling units with different secondary sampling units that were of different sizes. Results show that two-stage adaptive cluster sampling design is efficient compared to simple random sampling and the conventional two- stage sampling design. The design is less variable compared to the conventional two-stage sampling design.

Testing the Utility of an Adaptive Cluster Sampling Method for Monitoring a Rare and Imperiled Darter

AbstractAdaptive cluster sampling (ACS) designs were tested against simple random sampling (SRS) designs to determine whether ACS designs were more suitable sampling protocols for monitoring rare fish species. To test the utility of these designs, baseline data on the tuxedo darter Etheostoma lemniscatum (a rare, federally endangered fish) were collected at three sites on the Big South Fork of the Cumberland River and used in computer simulation of ACS designs. Based on the simulation models, five ACS designs were chosen and tested at 13 potential monitoring sites. In terms of efficiency, ACS designs performed better than SRS designs, providing estimates with smaller standard errors. Adaptive cluster sampling design efficiency increased with effort; therefore, the two goals—minimizing effort and maximizing accuracy—are incompatible. Because it had less error, an inverse ACS design was recommended, although it required more sampling effort than other designs. Factors possibly affecting overall design performance include the sample size, neighborhood configuration, and habitat complexity of sampling sites. This study was the first to implement ACS for rare and endangered stream‐dwelling fishes and provided methodologies for pilot testing and selecting appropriate ACS designs for an imperiled fish species. Adaptive cluster sampling designs are best suited for monitoring imperiled fishes that exhibit a more‐clustered spatial distribution. Population estimates from ACS designs using underwater observation provide quantitative data from standardized protocols that are applicable to long‐term monitoring of imperiled fishes.Received May 21, 2010; accepted June 21, 2011

Performance comparison of traditional sampling designs and adaptive sampling designs for fishery-independent surveys: A simulation study

We compared the performance of two traditional sampling designs with three adaptive sampling designs using simulated data based on fishery-independent surveys for yellow perch in Lake Erie. Traditionally, the fishery-independent survey has been conducted with a stratified random sampling design based on basin and depth strata; however, adaptive sampling designs are thought to be more suitable for surveying heterogeneous populations. A simulation study was conducted to compare these designs by examining the accuracy and precision of the estimators. Initially in the simulation study, we used bias, variance of the mean, and mean squared error (MSE) of the estimators to compare simple random sampling (SRS), stratified random sampling (StRS), and adaptive two-phase sampling (ATS). ATS was the best design according to these measurements. We then compared ATS, adaptive cluster sampling (ACS), adaptive two-stage sequential sampling (ATSS), and the currently used stratified random sampling design. ATS performed better than the other two approaches and the current stratified random sampling design. We concluded that ATS is preferable for yellow perch fishery-independent surveys in Lake Erie. Simulation study is a preferred approach when we seek an appropriate sampling design or evaluate the current sampling design.

An adaptive sampling method based on optimized sampling design for fishery-independent surveys with comparisons with conventional designs

The adaptive cluster sampling method is widely applied in terrestrial systems; however, it is not suitable for fisheries surveys because of the high cost of unlimited sampling in practice. An adaptive approach is often used in fisheries surveys to allocate sampling effort, usually following a stratified random design. Development of an adaptive sampling method based on optimized sampling design (this design has been suggested by previous study for fishery-independent surveys) has been not yet carried out. An adaptive sampling method based on optimized sampling design using the criterion of minimization of the mean of the shortest distance (MMSD) in the first phase was constructed in this study and compared with five other sampling designs: simple random, stratified random, adaptive based on stratified sampling, systematic, and optimum design based on the MMSD criterion. This design performed neither the best nor the worst among the six sampling designs considered in this study, but its advantages were obvious when the sampling effort saved using this design was considered in the comparison. This method tends to be more flexible and find fish aggregations more precisely. It is based on a more objective sampling design in the first phase compared with other adaptive sampling designs based on stratified sampling designs. We suggest that this design be considered in developing fishery-independent survey programs.

Evaluation of single and two‐stage adaptive sampling designs for estimation of density and abundance of freshwater mussels in a large river

AbstractReliable estimates of abundance are needed to assess consequences of proposed habitat restoration and enhancement projects on freshwater mussels in the Upper Mississippi River (UMR). Although there is general guidance on sampling techniques for population assessment of freshwater mussels, the actual performance of sampling designs can depend critically on the population density and spatial distribution at the project site. To evaluate various sampling designs, we simulated sampling of populations, which varied in density and degree of spatial clustering. Because of logistics and costs of large river sampling and spatial clustering of freshwater mussels, we focused on adaptive and non‐adaptive versions of single and two‐stage sampling. The candidate designs performed similarly in terms of precision (CV) and probability of species detection for fixed sample size. Both CV and species detection were determined largely by density, spatial distribution and sample size. However, designs did differ in the rate that occupied quadrats were encountered. Occupied units had a higher probability of selection using adaptive designs than conventional designs. We used two measures of cost: sample size (i.e. number of quadrats) and distance travelled between the quadrats. Adaptive and two‐stage designs tended to reduce distance between sampling units, and thus performed better when distance travelled was considered. Based on the comparisons, we provide general recommendations on the sampling designs for the freshwater mussels in the UMR, and presumably other large rivers. Published in 2009 by John Wiley & Sons, Ltd.

Complete allocation sampling: an efficient and easily implemented adaptive sampling design

AbstractAdaptive sampling designs are becoming increasingly popular in environmental science, particularly for surveying rare and aggregated populations. An adaptive sample is one in which the survey design is modified, or adapted, in some way on the basis of information gained during the survey. There are many different adaptive survey designs that can be used to estimate animal and plant abundance. In adaptive cluster sampling, additional sample effort is allocated during the survey to the immediate neighborhood in which the species is found. In adaptive stratified sampling, additional sample effort is allocated during the survey to strata of high abundance. The appealing feature of these adaptive designs is that the field biologist gets to do what innately seems sensible when working with rare and aggregated populations—field effort is targeted around where the species is observed in the first wave of the survey. However, there are logistical challenges of applying this principle of targeted field effort while remaining in the framework of probability‐based sampling. We propose a simplified adaptive survey design that incorporates both targeting field effort and being logistically feasible. We show with a case study population of rockfish that complete allocation stratified sampling is a very efficient design.

Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

Using Spatial Uncertainty of Prior Measurements to Design Adaptive Sampling of Elevation Data

Field sampling can be a major expense for planning within-field management in precision agriculture. An efficient sampling strategy should address knowledge gaps, rather than exhaustively collect redundant data. Modification of existing schemes is possible by incorporating prior knowledge of spatial patterns within the field. In this study, spatial uncertainty of prior digital elevation model (DEM) estimates was used to locate adaptive re-survey regions in the field. An agricultural vehicle equipped with RTK-DGPS was driven across a 2.3 ha field area to measure the field elevation in a continuous fashion. A geostatistical simulation technique was used to simulate field DEMs using measurements with different pass intervals and to quantitatively assess the spatial uncertainty of the DEM estimates. The high-uncertainty regions for each DEM were classified using image segmentation methods, and an adaptive re-survey was performed on those regions. The addition of adaptive re-surveying substantially reduced the time required to resample and resulted in DEMs with lower error. For the widest sampling pass width, the RMSE of 0.46 m of the DEM produced from an initial coarse sampling survey was reduced to 0.25 m after an adaptive re-survey, which was close to that (0.22 m) of the DEM produced with an all-field re-survey. The estimated sampling time for the adaptive re-survey was less than 50% of that for all-field re-survey. These results indicate that spatial uncertainty models are useful in an adaptive sampling design to help reduce sampling cost while maintaining the accuracy of the measurements. The method is general and thus not limited to elevation data but can be extended to other spatially variable field data.

On Using Adaptive Cluster Sampling Design in Forest Inventory: It's Implication to Forest Biodiversity Status Reporting

This paper presents adaptive cluster sampling (ACS) as a method of assessing forest biodiversity. In this study, ACS was used to estimate the abundance of ecologically sparse population of Diospyros philippinensis (Desrousseaux) within the Visayas State University Forest Reserve. Its statistical efficiency were analyzed by comparing them to the conventional systematic sampling (Syst) estimator. Results indicated that adaptive cluster sampling (ACS) plots captured more trees into the sample compared to systematic sampling (Syst) plots. In addition, ACS estimates for mean and total numbers of individuals per ha was higher than systematic sampling estimates and in terms of variance ACS gave substantially lower variance than systematic sampling. However, the ratio of the adjusted SE of ACS to the adjusted SE of systematic sampling for each species and the combined data of the two species was generally lesser than 1 which means that ACS was not a better design than systematic sampling.