Adjusted two-stage adaptive cluster sampling

An adjusted two-stage sampling procedure is discussed for adaptive cluster sampling where some networks are large and others are small. A two-stage sample is drawn from the large networks and a single-stage sample is drawn from the rest. The simple random sampling (SRS) procedure without replacement is used at the initial stage. An estimator for the population mean along with its properties is discussed.     

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.     

Restricted adaptive cluster sampling

Adaptive cluster sampling can be a useful design for sampling rare and patchy populations. With this design the initial sample size is fixed but the size of the final sample (and total sampling effort) cannot be predicted prior to sampling. For some populations the final sample size can be quite variable depending on the level of patchiness. Restricted adaptive cluster sampling is a proposed modification where a limit is placed on the sample size prior to sampling and quadrats are selected sequentially for the initial sample size. As a result there is less variation in the final sample size and the total sampling effort can be predicted with some certainty, which is impor- tant for many ecological studies. Estimates of density are biased with the restricted design but under some circumstances the bias can be estimated well by bootstrapping. © Rapid Science 1998     

Asymptotics in adaptive cluster sampling

In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators.     

Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Habitat association studies in conjunction with adaptive cluster samples

Habitat association studies investigate the relationships between habitat characteristics and animal usage of study regions. These studies are often conducted in conjunction with surveys designed primarily to estimate population totals. This paper shows that habitat association studies may proceed from surveys using adaptive cluster sampling. The manner in which units appear in the sample turns out not be relevant to the habitat association study, which proceeds as though the units came from a simple random sample. However, it is also shown that the information about the habitat association parameters is greater than one would expect from a simple random sample of the same general size.     

Comparison of a two-stage sampling design and its composite sample alternative: An application to soil studies

The objective of a long-term soil survey is to determine the mean concentrations of several chemical parameters for the pre-defined soil layers and to compare them with the corresponding values in the past. A two-stage random sampling procedure is used to achieve this goal. In the first step, n subplots are selected from N subplots by simple random sampling without replacement; in the second step, m sampling sites are chosen within each of the n selected subplots. Thus n · m soil samples are collected for each soil layer. The idea of the composite sample design comes from the challenge of reducing very expensive laboratory analyses: m laboratory samples from one subplot and one soil layer are physically mixed to form a composite sample. From each of the n selected subplots, one composite sample per soil layer is analyzed in the laboratory, thus n per soil layer in total. In this paper we show that the cost is reduced by the factor m — 1 when instead of the two-stage sampling its composite sample alternative is used; however, the variance of the composite sample mean is increased. In the case of positive intraclass correlation the increase is less than 12.5%; in the case of negative intraclass correlation the increase depends on the properties of the variable as well. For the univariate case we derive the optimal number of subplots and sampling sites. A case study is discussed at the end.     

A review of adaptive cluster sampling: 1990–2003

Adaptive cluster sampling (ACS) is an adaptive sampling scheme which operates under the rule that when the observed value of an initially selected sampling unit satisfies some condition of interest, C, other additional units in some pre-defined accompanying neighborhood are also added to the sample. In turn, if any of these additional units satisfy C, then their corresponding unit neighborhoods are added to the sample as well, and so on. This process stops when no additional units satisfying C are encountered. This paper will provide a review of the major developments and issues in ACS since its introduction by Thompson (1990) [Journal of the American Statistical Association, 85, 1050–1059].     

Performance of adaptive cluster sampling estimators in a multivariate setting

Adaptive cluster sampling has been proven to perform well in a univariate setting, but it may not perform well when there are several parameters of interest. The efficiency of adaptive sampling when there are several variables of interest depends on the relationship of the variables with one another.     

Application of adaptive cluster sampling to low-density populations of freshwater mussels

Freshwater mussels appear to be promising candidates for adaptive cluster sampling because they are benthic macroinvertebrates that cluster spatially and are frequently found at low densities. We applied adaptive cluster sampling to estimate density of freshwater mussels at 24 sites along the Cacapon River, WV, where a preliminary timed search indicated that mussels were present at low density. Adaptive cluster sampling increased yield of individual mussels and detection of uncommon species; however, it did not improve precision of density estimates. Because finding uncommon species, collecting individuals of those species, and estimating their densities are important conservation activities, additional research is warranted on application of adaptive cluster sampling to freshwater mussels. However, at this time we do not recommend routine application of adaptive cluster sampling to freshwater mussel populations. The ultimate, and currently unanswered, question is how to tell when adaptive cluster sampling should be used, i.e., when is a population sufficiently rare and clustered for adaptive cluster sampling to be efficient and practical? A cost-effective procedure needs to be developed to identify biological populations for which adaptive cluster sampling is appropriate.     

Rao-Blackwell versions of the Horvitz-Thompson and Hansen-Hurwitz in adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design and developed two unbiased estimators, the modified Horvitz-Thompson (HT) and Hansen-Hurwitz (HH) estimators, for this sampling design and noticed that these estimators are not a function of the minimal sufficient statistics. He applied the Rao-Blackwell theorem to improve them. Despite having smaller variances, these latter estimators have not received attention because a suitable method or algorithm for computing them was not available. In this paper we obtain closed forms of the Rao-Blackwell versions which can easily be computed. We also show that the variance reduction for the HH estimator is greater than that for the HT estimator using Rao-Blackwell versions. When the condition for extra samples is 0$$ " align="middle" border="0"> , one can expect some Rao-Blackwell improvement in the HH estimator but not in the HT estimator. Two examples are given.     

Effects of sample survey design on the accuracy of classification tree models in species distribution models

We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by resubstitution rates were similar for each lichen species irrespective of the underlying sample survey form. Cross-validation estimates of prediction accuracies were lower than resubstitution accuracies for all species and both design types, and in all cases were closer to the true prediction accuracies based on the EVALUATION data set. We argue that greater emphasis should be placed on calculating and reporting cross-validation accuracy rates rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE tree models on the EVALUATION data set shows significantly lower prediction accuracy for the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic sample surveys may generate models with limited predictive capability. These differences were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in accuracy were as large as 50%. The classification tree structures also differed considerably both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on non-probabilistic sample surveys.     

Identification of the largest individual sample value using composite sample data and certain modifications of the sweep-out method

Cost-effective hotspot identification is an important issue in hazardous waste site characterization and evaluation. Composite sampling techniques are known to be cost effective when the cost of measurement is substantially higher than the cost of sampling. Although compositing incurs no loss of information on the means, information on individual sample values is lost due to compositing. In particular, if the interest is in identifying the largest individual sample value, the composite sampling techniques are not able to do so. Under certain assumptions, it may be possible to satisfactorily predict individual sample values using the composite sample data, but it is not generally possible to identify the largest individual sample value. In this paper, we propose two methods of identifying the largest individual sample value with some additional measurement effort. Both methods are modifications of the simple sweep-out method proposed earlier. Since analytical results do not seem to be feasible, performance of the proposed methods is assessed via simulation. The simulation results show that both the proposed methods, namely the locally sequential sweep-out and the globally sequential sweep-out, are better than the simple sweep-out method.Prepared with partial support from the Statistical Analysis and Computing Branch, Environmental Statistics and Information Division, Office of Policy, Planning, and Evaluation, United States Environmental Protection Agency, Washington, DC under a Cooperative Agreement Number CR-821531. The contents have not been subjected to Agency review and therefore do not necessarily reflect the views of the Agency and no official endorsement should be inferred.     

The adaptive significance of male polymorphism in the acarid mite Caloglyphus berlesei

Summary Two forms of males occur in the acarid mite, Caloglyphus berlesei. One of them uses its thickened third pair of legs to kill other males; the other, without modified legs, does not attack other males. Previous studies have shown that the form of the male is environmentally determined: fighter males develop only at low population densities and their development can be suppressed by substances emanating from dense colonies. In this study, the duration of development, longevity and virility of the two male morphs were measured. The only significant difference was that fighters had a shorter development time between the two last moults. In another experiment, two groups of colonies were maintained under the same conditions but had different numbers of individuals: small colonies contained 2 fighters and 2 non-fighters, whereas large colonies contained 30 males of each type. The relative reproductive success of both morphs was estimated from numbers of matings. In small colonies, the estimated reproductive success (ERS) was significantly higher for fighters than for non-fighters, mainly because in over 50% of these colonies a single fighter male managed to kill all the rival males and monopolize the females. The opposite was true in large colonies, in which non-fighters achieved significantly higher ERS, mainly because the fighters were killed in fights more often than the non-fighters. This implies that the ratio of costs to benefits obtained by adopting the fighter-male strategy increases with the number of rival males, which may explain conditional male development in C. berlesei.     

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.     

Forks in the Road: Choices in Procedures for Designing Wildland Linkages

Abstract:  Models are commonly used to identify lands that will best maintain the ability of wildlife to move between wildland blocks through matrix lands after the remaining matrix has become incompatible with wildlife movement. We offer a roadmap of 16 choices and assumptions that arise in designing linkages to facilitate movement or gene flow of focal species between 2 or more predefined wildland blocks. We recommend designing linkages to serve multiple (rather than one) focal species likely to serve as a collective umbrella for all native species and ecological processes, explicitly acknowledging untested assumptions, and using uncertainty analysis to illustrate potential effects of model uncertainty. Such uncertainty is best displayed to stakeholders as maps of modeled linkages under different assumptions. We also recommend modeling corridor dwellers (species that require more than one generation to move their genes between wildland blocks) differently from passage species (for which an individual can move between wildland blocks within a few weeks). We identify a problem, which we call the subjective translation problem, that arises because the analyst must subjectively decide how to translate measurements of resource selection into resistance. This problem can be overcome by estimating resistance from observations of animal movement, genetic distances, or interpatch movements. There is room for substantial improvement in the procedures used to design linkages robust to climate change and in tools that allow stakeholders to compare an optimal linkage design to alternative designs that minimize costs or achieve other conservation goals.     

Designing environmental monitoring networks to measure extremes

This paper discusses challenges arising in the design of networks for monitoring extreme values over the domain of a random environmental space-time field {X _ij } i = 1, . . . , I denoting site and j = 1, . . . denoting time (e.g. hour). The field of extremes for time span r over site domain i = 1, . . . ,I is given by \(\{Y_{i(r+1)}=\max_{j=k}^{k+n-1} X_{ij}\}\) for k = 1 + rn, r = 0, . . . ,. Such networks must not only measure extremes at the monitored sites but also enable their prediction at the non-monitored ones. Designing such a network poses special challenges that do not seem to have been generally recognized. One of these problems is the loss of spatial dependence between site responses in going from the environmental process to the field of extremes it generates. In particular we show empirically that the intersite covariance Cov(Y _i(r+1),Y _i′(r+1)) can generally decline toward zero as r increases, for site pairs i ≠ i′. Thus the measured extreme values may not predict the unmeasured ones very precisely. Consequently high levels of pollution exposure of a sensitive group (e.g. school children) located between monitored sites may be overlooked. This potential deficiency raises concerns about the adequacy of air pollution monitoring networks whose primary role is the detection of noncompliance with air quality standards based on extremes designed to protect human health. The need to monitor for noncompliance and thereby protect human health, points to other issues. How well do networks designed to monitor the field monitor their fields of extremes? What criterion should be used to select prospective monitoring sites when setting up or adding to a network? As the paper demonstrates by assessing an existing network, the answer to the first question is not well, at least in the case considered. To the second, the paper suggests a variety of plausible answers but shows through a simulation study, that they can lead to different optimum designs. The paper offers an approach that circumvents the dilemma posed by the answer to the second question. That approach models the field of extremes (suitably transformed) by a multivariate Gaussian-Inverse Wishart hierarchical Bayesian distribution. The adequacy of this model is empirically assessed in an application by finding the relative coverage frequency of the predictive credibility ellipsoid implied by its posterior distribution. The favorable results obtained suggest this posterior adequately describes that (transformed) field. Hence it can form the basis for designing an appropriate network. Its use is demonstrated by a hypothetical extension of an existing monitoring network. That foundation in turn enables a network to be designed of sufficient density (relative to cost) to serve its regulatory purpose.     

我国丹顶鹤自然保护区网络设计

针对原有丹顶鹤保护区规划缺乏系统设计思想,保护区面临严重的生境安全这一问题,根据维持生态系统地域完整性和生态过程完整性的原则,采用迭代法和整数规划2种方法,以高、中适宜性湿地面积占各自湿地类型总面积70%和60%为保护目标,研究了丹顶鹤自然保护区的网络设计,提出了丹顶鹤自然保护区网络的设计方案。     

Order restricted randomized designs and two sample inference

This paper develops a new design that relies on subjective judgment ranking to compare subsets of experimental units. This judgment ranking is used along with restricted randomization to improve statistical inference for the contrast between two levels of a treatment. The new design assigns the judgment ranked units in a subset to different treatments. Such an assignment translates the positive dependence among units within each subset into negative dependence for the estimators of treatment means, and hence leads to a reduction in variance for the contrast. For the proposed design, a test for the difference in means of two treatment levels is developed along with an associated confidence interval. It is shown that the null distribution of the proposed test is approximated reasonably well with the Student’s t-distribution for sample sizes as small as 6. A simulation study indicates that the proposed design is advantageous compared to its competitors in the literature for both high and low quality rankings. The new design’s advantage increases with the quality of rankings.