Adaptive Sampling Designs Research Articles

Effect of imperfect detectability on adaptive and conventional sampling: simulated sampling of freshwater mussels in the upper Mississippi River

Adaptive sampling designs are recommended where, as is typical with freshwater mussels, the outcome of interest is rare and clustered. However, the performance of adaptive designs has not been investigated when outcomes are not only rare and clustered but also imperfectly detected. We address this combination of challenges using data simulated to mimic properties of freshwater mussels from a reach of the upper Mississippi River. Simulations were conducted under a range of sample sizes and detection probabilities. Under perfect detection, efficiency of the adaptive sampling design increased relative to the conventional design as sample size increased and as density decreased. Also, the probability of sampling occupied habitat was four times higher for adaptive than conventional sampling of the lowest density population examined. However, imperfect detection resulted in substantial biases in sample means and variances under both adaptive sampling and conventional designs. The efficiency of adaptive sampling declined with decreasing detectability. Also, the probability of encountering an occupied unit during adaptive sampling, relative to conventional sampling declined with decreasing detectability. Thus, the potential gains in the application of adaptive sampling to rare and clustered populations relative to conventional sampling are reduced when detection is imperfect. The results highlight the need to increase or estimate detection to improve performance of conventional and adaptive sampling designs.

An adaptive allocation sampling design for which the conventional stratified estimator is an appropriate estimator

Adaptive allocations in stratified sampling design are suitable for studying Biological and Environmental populations. Biologists tend to use the conventional stratified estimator for an adaptive allocation sampling design in spite of its adaptive nature. In this paper, we have introduced an adaptive allocation sampling design for which the conventional stratified estimator has some desired statistical properties. We conduct a simulation study on a real population. The results show that the conventional stratified estimator for the introduced adaptive allocation sampling design is more efficient than other available estimators.

Effect of Adaptive Cluster Sampling Design on Accuracy of Sediment Rating Curve Estimation

Adaptive cluster sampling represents a design whereby more samples during high storm hydrographs can be obtained in the field compared to the commonly used calendar-based. To compare the effect of these sampling designs on accuracy of sediment rating curve estimation, we performed a study for Gorgan-Rood River, Iran by synthesizing sample sets from daily records. The load estimates obtained by conventional, two bias-corrected, and logged mean load within discharge classes (LMLWDCs) rating curves were statistically evaluated. All rating curves derived from calendar-based sample sets–except those with a nonparametric correction factor–underestimated the average load from 25 to 76%. Rating curves derived from adaptive sample sets, however, increased the sediment load to as much as 30%. Among this group of rating curves, LMLWDC produced the most accurate results with only 3% overestimation and a coefficient of variation in the order of 14% when the sampling frequency was semiweekly. The more accurate estimates from adaptive sample sets are likely due to the inclusion of more samples from high load periods.

Algorithms for response adaptive sampling designs

AbstractAn experimental design is a formula or algorithm that specifies how resources are to be utilized throughout a study. The design is considered to be good or even optimal if it allows for sufficiently precise and accurate data analysis with the least output of resources such as time, money and experimental units. Most experimental designs use fixed sampling procedures in which the sample sizes and order of allocations to different study groups are known in advance. Copyright © 2009 John Wiley & Sons, Inc.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Sampling

Efficient estimators for adaptive stratified sequential sampling

In stratified sampling, methods for the allocation of effort among strata usually rely on some measure of within-stratum variance. If we do not have enough information about these variances, adaptive allocation can be used. In adaptive allocation designs, surveys are conducted in two phases. Information from the first phase is used to allocate the remaining units among the strata in the second phase. Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation sampling design – where the final sample size was random – and an unbiased estimator. Here, we derive an unbiased variance estimator for the design, and consider a related design where the final sample size is fixed. Having a fixed final sample size can make survey-planning easier. We introduce a biased Horvitz–Thompson type estimator and a biased sample mean type estimator for the sampling designs. We conduct two simulation studies on honey producers in Kurdistan and synthetic zirconium distribution in a region on the moon. Results show that the introduced estimators are more efficient than the available estimators for both variable and fixed sample size designs, and the conventional unbiased estimator of stratified simple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator with the introduced estimators. Simulation results show that the introduced estimators are more efficient than available estimators of these well-known adaptive allocation designs.

Evaluation of Sampling Designs for Red Sea Urchins Strongylocentrotus franciscanus in British Columbia

AbstractEstimates of the total stock biomass of marine invertebrates that aggregate, such as red sea urchins Strongylocentrotus franciscanus, are often highly uncertain, partly because it is difficult to estimate their density. To improve estimates, we used 200 simulated red sea urchin populations with spatial and numerical properties based on field data to evaluate various simulated survey designs for a given number of transects in terms of the precision, bias, and efficiency (relative variance) of their estimates. We considered a random transect sampling method that is currently used in British Columbia for red sea urchins, which samples every other quadrat within each transect, as well as a complete version of that transect method, which samples every quadrat. We also evaluated more complex random transect sampling designs, including restricted adaptive cluster sampling and a design stratified by type of substrate within each transect. The complete transect method produced essentially unbiased estimates of red sea urchin density (as did the currently used sampling design) and had lower variance than the current method, but the complete method used twice as many quadrat samples per transect to do so (incurring higher costs of sampling by divers). In contrast, the design stratified by substrate required 33% fewer sampled quadrats per transect than the current sampling method to achieve the same variance as that method, but it had a median bias of 10%. Finally, the restricted adaptive cluster sampling design gave estimates that had lower variance than the current method and used 18% fewer sampled quadrats, but the median urchin density estimate was biased downward by 8%. Choosing among sampling designs thus involves making trade‐offs among bias, precision, and sampling cost as well as considering practical constraints on scuba divers who attempt to implement complex designs in field situations.

적응집락추출에서 표본크기 결정과 추정량의 효율 비교

모집단 단위들이 희박하게 존재하고 접근하기 어려운 경우에 적용하는 적응추출설계에서의 추출과정은 관심변수의 관측값에 의존한다. 동일한 표본크기에서 적응집락추출의 추정량은 단순임의추출의 추정량에 비해 효율이 더 좋다 적응추출에서 Rao-blackwell의 정리를 적용하여 Murthy의 추정량의 형태로 수정한 한센-휴비_(HH) 추정량과 호르비_-톰슨 (HT) 추정량은 기존의 추정량에 비해 작은 분산을 가진다. 본 연구는 초기표본을 바꿔가면서 기대표본크기와 적응추출의 표본크기 하의 단순임의추출의 추정량과 적응추출의 추정량의 효율을 비교하였다. Adaptive sampling design is the selection procedure which depends on observed values of the variable of interest. It is the method which could be applied to the rare and unapproachable population. Adaptive cluster sampling strategies are more efficient than simple random sampling on equivalent sample size. Adaptive sampling with new estimators through the Rao-blackwell method have lower variance than Horvitz-Thompson (HT) and Hansen-Hurwitz (HH). Also, to determine suitable sample size, it was used expected sample and the method finding appropriate sample size by changing initial sample size were studied.

Influence of adaptive stations in a transect-based sampling design for a multispecies fish survey

A multispecies transect-based survey with an adaptive sampling design was evaluated to determine the import of adding stations adaptively at sea in order to better resolve the cross-shelf distribution of species in regions of rapid bathymetric change. The dataset came from a series of transects occupied in November, January, March, and May from May 2003 to November 2005 along transects northeast of Hudson Canyon and northeast of Baltimore Canyon in the Mid-Atlantic Bight region of the western Atlantic. The transect survey results demonstrate the necessity of high sample density in this region of the continental shelf where fish aggregate patchily over scales of a few kilometers. Species cross-shelf distributions were often bimodal. The adaptive sampling protocol demonstrated the expected tendency of fish to be underestimated or overestimated given inadequate sampling density. However, on the average, low sample density led to an underestimation of biomass or abundance and often strongly so. Modeling of the transect design reveals that the overestimates and underestimates, as well as the bias towards underestimation, originate from variations in patch location and, even more importantly, patch shape, with the sampling design. The transect model shows that extreme overestimates and underestimates can occur when patch size is small relative to the distance between stations, but the occurrence of routine, predictable, persistent underestimates in some species is not so easily explained. The model clearly resolves the importance of bimodality and a patch form represented by a dome shape in determining the vulnerability of a species to a biomass or abundance underestimate. Cases where the fixed stations alone provide data clearly inadequate for the estimate of abundance or biomass occur when sampling density is inadequate to identify the center of the patch or to identify the shape of the patch. It is the improved understanding of patch shape that is the single most important contribution of the adaptive sampling protocol, not a better knowledge of the location of the patches. Patch shape is a principal determinant of the adequacy of sample density.

Ratio estimators in adaptive cluster sampling

AbstractIn most surveys data are collected on many items rather than just the one variable of primary interest. Making the most use of the information collected is a issue of both practical and theoretical interest. Ratio estimates for the population mean or total are often more efficient. Unfortunately, ratio estimation is straightforward with simple random sampling, but this is often not the case when more complicated sampling designs are used, such as adaptive cluster sampling. A serious concern with ratio estimates introduced with many complicated designs is lack of independence, a necessary assumption. In this article, we propose two new ratio estimators under adaptive cluster sampling, one of which is unbiased for adaptive cluster sampling designs. The efficiencies of the new estimators to existing unbiased estimators, which do not utilize the auxiliary information, for adaptive cluster sampling and the conventional ratio estimation under simple random sampling without replacement are compared in this article. Related result shows the proposed estimators can be considered as a robust alternative of the conventional ratio estimator, especially when the correlation between the variable of interest and the auxiliary variable is not high enough for the conventional ratio estimator to have satisfactory performance. Copyright © 2007 John Wiley & Sons, Ltd.

Adaptive Web Sampling

A flexible class of adaptive sampling designs is introduced for sampling in network and spatial settings. In the designs, selections are made sequentially with a mixture distribution based on an active set that changes as the sampling progresses, using network or spatial relationships as well as sample values. The new designs have certain advantages compared with previously existing adaptive and link-tracing designs, including control over sample sizes and of the proportion of effort allocated to adaptive selections. Efficient inference involves averaging over sample paths consistent with the minimal sufficient statistic. A Markov chain resampling method makes the inference computationally feasible. The designs are evaluated in network and spatial settings using two empirical populations: a hidden human population at high risk for HIV/AIDS and an unevenly distributed bird population.

Adaptation of multiple logistic regression to a multiple inverse sampling design: application to the Isfahan healthy heart program

In observational and experimental studies in the health sciences involving human populations, it is sometimes considered desirable to recruit subjects according to designs that specify a predetermined number of subjects in each of several mutually exclusive classes (generally but not necessarily demographic in nature). This type of adaptive sampling design, now generally referred to as multiple inverse sampling (MIS), has received recent attention, and estimation methods are now available for several sequential MIS sampling designs. In this class of designs, subjects are sampled randomly and sequentially, usually one at a time, until all classes have the pre-specified number of subjects. In this paper, we extend MIS for finite population sampling to estimation of the parameters in multiple logistic regression under MIS. Using estimated logistic regression parameters and cost components obtained from the Isfahan Healthy Heart Program (IHHP), we report findings from a simulation experiment in which it appears that, at fixed cost, MIS at the last stage of sampling compares favourably to simple random sampling. The IHHP is a large community intervention study for prevention of cardiovascular disease being conducted in Isfahan, Iran and two other cities in Iran. The IHHP identified subjects through a multistage sample survey in which MIS was used at the final stage of sampling. MIS is one of several methods of adaptive sampling that are generating considerable interest and show promise of being useful in a wide variety of applications.

Adaptive cluster double sampling

We present a multi-phase variant of adaptive cluster sampling which allows the sampler to control the number of measurements of the variable of interest. A first-phase sample is selected using an adaptive cluster sampling design based on an inexpensive auxiliary variable associated with the survey variable. Then the network structure of the adaptive cluster sample is used to select an ordinary one-phase or two-phase subsample of units and the values of the survey variable associated with those units are recorded. The population mean is estimated by either a regression-type estimator or a Horvitz–Thompson-type estimator. The results of a simulation study show good performance of the proposed design, and suggest that in many real situations this design might be preferred to the ordinary adaptive cluster sampling design.

Using the bootstrap with two-phase adaptive stratified samples from multiple populations at multiple locations

Recently the two-phase adaptive stratified sampling design proposed by Francis (1984) has been extended by Manly et al. (2002) for situations where several biological populations are sampled simultaneously, and where this is done at several different geographical locations in order to estimate population totals or means. The method uses the results from a first phase sample to decide how best to allocate a second phase sample to locations and strata, in order to maximise a criterion (based on estimated coefficients of variation) that measures the accuracy of estimation for population totals, for all variables at all locations. One potential problem with this method is bias in the estimators of the population totals and means. In this paper bootstrapping is considered as a means of overcoming these biases. It is shown using model populations of Pacific walrus and shellfish, based on real data, that bootstrapping is a useful tool for removing about half of the bias. This is also confirmed from some simulations using artificial data.

Effect of sampling design on abundance estimates of benthic invertebrates in environmental monitoring studies

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 276:19-24 (2004) - doi:10.3354/meps276019 Effect of sampling design on abundance estimates of benthic invertebrates in environmental monitoring studies Henrique N. Cabral1,*, Alberto G. Murta2 1Instituto de Oceanografia and Departamento de Biologia Animal, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal 2Departamento de Recursos Marinhos, INIAP-IPIMAR, Avenida de Brasília, 1449-006 Lisboa, Portugal *Email: hcabral@fc.ul.pt ABSTRACT: Random, stratified, systematic and adaptative sampling designs were analyzed comparatively using data of benthic invertebrate abundance in the mudflats of the Tagus estuary. Intensive core sampling was performed in spring and summer of 1996, in an area of 4 m2. Estimates determined from sub-sets of samples chosen using the various designs were compared. The mean values of the density estimates obtained by the various sampling designs and sample sizes differed significantly, and the main variation trends also differed according to species. For species with low abundace, i.e. Polydora ciliata and Sphaeroma monodi, the estimates obtained by random sampling (RS), systematic sampling (SyS) and stratified sampling (SS) were similar to the real density value, while those that resulted from the adaptive sampling (AS) design tended to overestimate density in the majority of cases. A different pattern was obtained for the abundant species, i.e. Streblospio shrubsolii and Scrobicularia plana. For these species, the mean values of the estimates obtained by RS, SyS and SS were similar and presented a negligible bias, although their variances were usually high. AS designs produced strongly biased estimates, although with low variance. The mean values of these estimates were considerably lower than the true mean density value. Comparison of the mean variance estimates for the sample sizes considered for each sampling design with the RS variance estimates revealed that the lowest variance ratios were obtained with SS designs. KEY WORDS: Sampling design · Sample size · Adaptive sampling · Benthic invertebrates · Environmental monitoring Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 276. Online publication date: August 02, 2004 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2004 Inter-Research.

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.

Comparison between Hansen-Hurwitz and Horvitz-Thompson estimators for adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design. This sampling design has been shown to be a useful sampling method for parameter estimation of a clustered and scattered population (Roesch, 1993; Smith et al., 1995; Thompson and Seber, 1996). Two estimators, the modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators, are available to estimate the mean or total of a population. Empirical results from previous researches indicate that the modified HT estimator has smaller variance than the modified HH estimator. We analytically compare the properties of these two estimators. Some results are obtained in favor of the modified HT estimator so that practitioners are strongly recommended to use the HT estimator despite easiness of computations for the HH estimator.

Adaptive sampling in research on risk-related behaviors

This article introduces adaptive sampling designs to substance use researchers. Adaptive sampling is particularly useful when the population of interest is rare, unevenly distributed, hidden, or hard to reach. Examples of such populations are injection drug users, individuals at high risk for HIV/AIDS, and young adolescents who are nicotine dependent. In conventional sampling, the sampling design is based entirely on a priori information, and is fixed before the study begins. By contrast, in adaptive sampling, the sampling design adapts based on observations made during the survey; for example, drug users may be asked to refer other drug users to the researcher. In the present article several adaptive sampling designs are discussed. Link-tracing designs such as snowball sampling, random walk methods, and network sampling are described, along with adaptive allocation and adaptive cluster sampling. It is stressed that special estimation procedures taking the sampling design into account are needed when adaptive sampling has been used. These procedures yield estimates that are considerably better than conventional estimates. For rare and clustered populations adaptive designs can give substantial gains in efficiency over conventional designs, and for hidden populations link-tracing and other adaptive procedures may provide the only practical way to obtain a sample large enough for the study objectives.

Spatial structure, sampling design and abundance estimates in sandy beach macroinfauna: some warnings and new perspectives

We discuss methodological aspects directed to quantify the across-shore population structure and abundance of sandy beach macroinfauna. The reliability of estimates derived from design-based (stratified random sampling) and model-based (geostatistics, kriging) approaches is discussed. Our analysis also addresses potential biases arising from environmentally driven designs that consider a priori fixed strata for sampling macroinfauna, as opposed to species-driven sampling designs, in which the entire range of across-shore distribution is covered. Model-based approaches showed, spatially, highly autocorrelated and persistent structures in two intertidal populations of the Uruguayan coast: the isopod Excirolanaarmata and the yellow clam Mesodesmamactroides. Both populations presented zonation patterns that ranged from the base of the dunes to upper levels of the subtidal. The Gaussian model consistently explained the spatial distribution of species and population components (clam recruits and adults), with a minor contribution (≤5%) of unresolved, small-scale variability. The consistent structure of spatial dependence in annual data strongly suggests an across-shore-structured process covering close to 35 m. Kriging predictions through cross-validation corroborated the appropriateness of the models fitted through variographic analysis, and the derived abundance estimates were very similar (maximum difference=7%) to those obtained from linear interpolation. Monthly analysis of E. armata data showed marked variations in its zonation and an unstable spatial structure according to the Gaussian model. The clear spatial structure resulting from species-driven sampling was not observed when data was truncated to simulate an environmentally driven sampling design. In this case, the linear semivariogram indicated a spatial gradient, suggesting that sampling was not performed at the appropriate spatial scale. Further, the cross-validation procedure was not significant, and both density and total abundance were underestimated. We conclude that: (1) geostatistics provides useful additional information about population structure and aids in direct abundance estimation; thus we suggest it as a powerful tool for further applications in the study of sandy beach macroinfauna; and that (2) environmentally driven sampling strategies fail to provide conclusive results about population structure and abundance, and should be avoided in studies of sandy beach populations. This is especially true for microtidal beaches, where unpredictable swash strength precludes a priori stratification through environmental reference points. The need to use adaptive sampling designs and avoid snapshot sampling is also stressed. Methodological implications for the detection of macroecological patterns in sandy beach macroinfauna are also discussed.

Theory & Methods: Unbiased estimators for restricted adaptive cluster sampling

In adaptive cluster sampling the size of the final sample is random, thus creating design problems. To get round this, Brown (1994) and Brown & Manly (1998) proposed a modification of the method, placing a restriction on the size of the sample, and using standard but biased estimators for estimating the population mean. But in this paper a new unbiased estimator and an unbiased variance estimator are proposed, based on estimators proposed by Murthy (1957) and extended to sequential and adaptive sampling designs by Salehi & Seber (2001). The paper also considers a restricted version of the adaptive scheme of Salehi & Seber (1997a) in which the networks are selected without replacement, and obtains unbiased estimators. The method is demonstrated by a simple example. Using simulation from this example, the new estimators are shown to compare very favourably with the standard biased estimators.

Improved sampling of wildlife populations using airborne surveys

Parameter estimates, obtained from airborne surveys of wildlife populations, often have large bias and large standard errors. Sampling error is one of the major causes of this imprecision and the occurrence of many animals in herds violates the common assumptions in traditional sampling designs like systematic or simple random sampling even when stratification is used. In this paper, we present an adaptive sampling design that uses criteria of observed animal counts to maximise sample information and that is independent of the usual assumption of a uniform distribution for wildlife populations. For illustration, the design is applied to data derived from a survey carried out in the Masai Mara ecosystem (Mara) of Kenya, with a focus on three species: elephant (Loxodonta africana), kongoni (Alcelaphus buselaphus) and wildebeest (Connochaetes taurinus). The sampling design's more efficient estimates show an improvement on those from conventional systematic design, with a greater than 10 times reduction in estimated bias and a 37% lowering of the standard error. The adaptive design, however, underestimates population totals for species in large herds, while a multivariate extension gives only marginal improvements.