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.     

Use of best linear unbiased prediction for hot spot identification in two-way compositing

Compositing of individual samples is a cost-effective method for estimating a population mean, but at the expense of losing information about the individual sample values. The largest of these sample values (hotspot) is sometimes of particular interest. Sweep-out methods attempt to identify the hotspot and its value by quantifying a (hopefully, small) subset of individual values as well as the usual quantification of the composites. Sweep-out design is concerned with the sequential selection of individual samples for quantification on the basis of all earlier quantifications (both composite and individual). The design-goal is for the number of individual quantifications to be small (ideally, minimal). Previous sweep-out designs have applied to traditional (i.e., disjoint) compositing. This paper describes a sweep-out design suitable for two-way compositing. That is, the individual samples are arranged in a rectangular array and a composite is formed from each row and also from each column. At each step, the design employs all available measurements (composite and individual) to form the best linear unbiased predictions for the currently unquantified cells. The cell corresponding to the largest predicted value is chosen next for individual measurement. The procedure terminates when the hotspot has been identified with certainty.     

Identifying the largest individual sample value from a two-way composite sampling design

Composite sampling techniques for identifying the largest individual sample value seem to be cost effective when the composite samples are internally homogeneous. However, since it is not always possible to form homogeneous composite samples, these methods can lead to higher costs than expected. In this paper we propose a two-way composite sampling design as a way to improve on the cost effectiveness of the methods available to identify the largest individual sample value.     

Composite sampling: A novel method to accomplish observational economy in environmental studies: A monograph introduction

This monograph on composite sampling, co-authored by Patil, Gore, and Taillie provides, for the first time, a most comprehensive statistical account of composite sampling as an ingenious environmental sampling method to help accomplish observational economy in a variety of environmental and ecological studies. Sampling consists of selection, acquisition, and quantification of a part of the population. But often what is desirable is not affordable, and what is affordable is not adequate. How do we deal with this dilemma? Operationally, composite sampling recognizes the distinction between selection, acquisition, and quantification. In certain applications, it is a common experience that the costs of selection and acquisition are not very high, but the cost of quantification, or measurement, is substantially high. In such situations, one may select a sample sufficiently large to satisfy the requirement of representativeness and precision and then, by combining several sampling units into composites, reduce the cost of measurement to an affordable level. Thus composite sampling offers an approach to deal with the classical dilemma of desirable versus affordable sample sizes, when conventional statistical methods fail to resolve the problem. Composite sampling, at least under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. In this monograph, we present statistical solutions to these and other issues that arise in the context of applications of composite sampling. The monograph is published in the Monograph Series: Environmental and Ecological Statistics <http://www.springer.com/series/7506>, vol. 4, The authors are Patil, Ganapati P., Gore, Sharad D., Taillie, Charles with the monograph co-ordinates,1st Edition., 2011, XIII, 275 p. 47 illus., SpringerLink <http://www.springerlink.com/content/978-1-4419-7627-7>, Hardcover, >  ISBN 978-1-4419-7627-7.     

Quantifying the efficiency of soil sampling designs: A multivariate approach

The objective of this paper is to quantify and compare the loss functions of the standard two-stage design and its composite sample alternative in the context of multivariate soil sampling. The loss function is defined (conceptually) as the ratio of cost over information and measures design inefficiency. The efficiency of the design is the reciprocal of the loss function. The focus of this paper is twofold: (a) we define a measure of multivariate information using the Kullback–Leibler distance, and (b) we derive the variance-covariance structure for two soil sampling designs: a standard two-stage design and its composite sample counterpart. Randomness in the mass of soil samples is taken into account in both designs. A pilot study in Slovenia is used to demonstrate the calculations of the loss function and to compare the efficiency of the two designs. The results show that the composite sample design is more efficient than the two-stage design. The efficiency ratio is 1.3 for pH, 2.0 for C, 2.1 for N, and 2.5 for CEC. The multivariate efficiency ratio is 2.3. These ratios primarily reflect cost ratios; influence of the information is small.     

Editorial: Composite sampling

The high costs of laboratory analytical procedures frequently strain environmental and public health budgets. Whether soil, water or biological tissue is being analysed, the cost of testing for chemical and pathogenic contaminants can be quite prohibitive.Composite sampling can substantially reduce analytical costs because the number of required analyses is reduced by compositing several samples into one and analysing the composited sample. By appropriate selection of the composite sample size and retesting of select individual samples, composite sampling may reveal the same information as would otherwise require many more analyses.Many of the limitations of composite sampling have been overcome by recent research, thus bringing out more widespread potential for using composite sampling to reduce costs of environmental and public health assessments while maintaining and often increasing the precision of sample-based inference.     

The use of composite sampling in contaminated sites—a case study

Simulated composite sampling was carried out using data from a contaminated site. The values obtained by composite sampling were compared with the results obtained using discrete (individual) samples. It is appropriate to use a modified investigation level (MIL) when using composite samples. The MIL is lower than the standard investigation level, (IL). Various MILs were considered in this study. Too low an MIL will indicate that some composite samples require further investigation, when none of the discrete samples comprising the composite would have exceeded the IL. Too high an MIL will result in some discrete samples that exceed the IL being missed. A suggested MIL is IL/ where n is the number of discrete samples in the composite sample. This MIL was found to give few false negatives but many fewer false positives than the IL/n rule. Although this MIL was effective on the test data it could be site specific. Some local areas of high concentration may be missed with composite samples if a lower investigation level is used. These however do not make a large contribution to the health risk because they will have a contaminant level only slightly higher than the IL, and the neighboring samples must have a low concentration of the contaminant. The increased risk due this cause may be more than offset by the higher sampling density made possible through the economies of composite sampling When composite sampling is used as the first phase of an adaptive cluster-sampling scheme, it must be augmented by additional samples to delineate the contaminated area to be cleaned up. Composite sampling can also be effectively used in a clean up unit technique, where a clean up unit is represented by one or more composite samples. Suggestions are given for when composite sampling can be used effectively.     

Sampling variability and estimates of density dependence: a composite-likelihood approach

It is well known that sampling variability, if not properly taken into account, affects various ecologically important analyses. Statistical inference for stochastic population dynamics models is difficult when, in addition to the process error, there is also sampling error. The standard maximum-likelihood approach suffers from large computational burden. In this paper, I discuss an application of the composite-likelihood method for estimation of the parameters of the Gompertz model in the presence of sampling variability. The main advantage of the method of composite likelihood is that it reduces the computational burden substantially with little loss of statistical efficiency. Missing observations are a common problem with many ecological time series. The method of composite likelihood can accommodate missing observations in a straightforward fashion. Environmental conditions also affect the parameters of stochastic population dynamics models. This method is shown to handle such nonstationary population dynamics processes as well. Many ecological time series are short, and statistical inferences based on such short time series tend to be less precise. However, spatial replications of short time series provide an opportunity to increase the effective sample size. Application of likelihood-based methods for spatial time-series data for population dynamics models is computationally prohibitive. The method of composite likelihood is shown to have significantly less computational burden, making it possible to analyze large spatial time-series data. After discussing the methodology in general terms, I illustrate its use by analyzing a time series of counts of American Redstart (Setophaga ruticilla) from the Breeding Bird Survey data, San Joaquin kit fox (Vulpes macrotis mutica) population abundance data, and spatial time series of Bull trout (Salvelinus confluentus) redds count data.     

Chernobyl as a population sink for barn swallows: tracking dispersal using stable-isotope profiles.

Stable-isotope profiles of feathers can reveal the location or habitat used by individual birds during the molting period. Heterogeneity in isotope profiles will reflect heterogeneity in molt locations, but also heterogeneity in breeding locations, because spatial heterogeneity in molt locations will be congruent with spatial heterogeneity in breeding locations in species with high connectivity between breeding and molting sites. We used information on the congruence of spatial heterogeneity in molt and breeding location to study population processes in Barn Swallows (Hirundo rustica) from a region. near Chernobyl, Ukraine, that has been radioactively contaminated since 1986; from an uncontaminated control region near Kanev, Ukraine; and from a sample of pre-1986 museum specimens used to investigate patterns prior to the nuclear disaster at Chernobyl, from both regions. Previous studies have revealed severe reductions in Barn Swallow reproductive performance and adult survival in the Chernobyl region, implying that the population is a sink and unable to sustain itself. Female Barn Swallows are known to disperse farther from their natal site than males, implying that female stable-isotope profiles should tend to be more variable than profiles of males. However, if the Barn Swallows breeding at Chernobyl are not self-sustaining, we would expect males there also to originate from a larger area than males from the control region. We found evidence that the sample of adult Barn Swallows from the Chernobyl region was more isotopically heterogeneous than the control sample, as evidenced from a significant correlation between feather sigma13C and sigma15N values in the control region, but not in the Chernobyl region. Furthermore, we found a significant difference in feather sigma15N values between regions and periods (before and after 1986). When we compared the variances in sigma13C values of feathers, we found that variances in both sexes from post-1986 samples from Chernobyl were significantly larger than variances for feather samples from the control region, and than variances for historical samples from both regions. These findings suggest that stable-isotope measurements can provide information about population processes following environmental perturbations.     

Resampling from stochastic simulations

To model the uncertainty of an estimate of a global property, the estimation process is repeated on multiple simulated fields, with the same sampling strategy and estimation algorithm. As opposed to conventional bootstrap, this resampling scheme allows for spatially correlated data and the common situation of preferential and biased sampling. The practice of this technique is developed on a large data set where the reference sampling distributions are available. Comparison of the resampled distributions to that reference shows the probability intervals obtained by resampling to be reasonably accurate and conservative, provided the original and actual sample has been corrected for the major biases induced by preferential sampling.Andre G. Journel is a Professor of Petroleum Engineering at Stanford University with a joint appointment in the Department of Geological and Environmental Sciences. He is, also, Director of the Stanford Center for Reservoir Forecasting. Professor Journel has pioneered applications of geostatistical techniques in the mining/petroleum industry and extended his expertise to environmental applications and repository site characterization. Most notably, he developed the concept of non-parametric geostatistics and stochastic imaging with application to modeling uncertainty in reservoir/site characterization. Although the research described in this article has been supported by the United States Environmental Protection Agency under Cooperative Agreement CR819407, it has not been subjected to Agency review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.     

Identifying landscape scale patterns from individual scale processes

Extrapolating across scales is a critical problem in ecology. Explicit mechanistic models of ecological systems provide a bridge from measurements of processes at small and short scales to larger scales; spatial patterns at large scales can be used to test the outcomes of these models. However, it is necessary to identify patterns that are not dependent on initial conditions, because small scale initial conditions will not normally be measured at large scales. We examined one possible pattern that could meet these conditions, the relationship between mean and variance in abundance of a parasitic tick in an individual based model of a lizard tick interaction. We scaled discrepancies between the observed and simulated patterns with a transformation of the variance–covariance matrix of the observed pattern to objectively identify patterns that are “close”.     

An effective dietary survey framework for the assessment of total dietary arsenic intake in Bangladesh: Part-A—FFQ design

Groundwater contaminated with arsenic (As), when extensively used for irrigation, causes potentially long term detrimental effects to the landscape. Such contamination can also directly affect human health when irrigated crops are primarily used for human consumption. Therefore, a large number of humans are potentially at risk worldwide due to daily As exposure. Numerous previous studies have been severely limited by small sample sizes which are not reliably extrapolated to large populations or landscapes. Human As exposure and risk assessment are no longer simple assessments limited to a few food samples from a small area. The focus of more recent studies has been to perform risk assessment at the landscape level involving the use of biomarkers to identify and quantify appropriate health problems and large surveys of human dietary patterns, supported by analytical testing of food, to quantify exposure. This approach generates large amounts of data from a wide variety of sources and geographic information system (GIS) techniques have been used widely to integrate the various spatial, demographic, social, field, and laboratory measured datasets. With the current worldwide shift in emphasis from qualitative to quantitative risk assessment, it is likely that future research efforts will be directed towards the integration of GIS, statistics, chemistry, and other dynamic models within a common platform to quantify human health risk at the landscape level. In this paper we review the present and likely future trends of human As exposure and GIS application in risk assessment at the landscape level.     

Use made in marine ecology of methods for estimating demographic parameters from size/frequency data

Macdonald and Pitcher's method of decomposing a sizefrequency histogram into cohorts (mathematical optimization of the fit of the distribution function to the histogram) has been used to estimate the composition of random samples drawn from populations with known cohort structure. The large-sample behaviour of the method is in accordance with the results of asymptotic theory. With sample sizes typical of those used in many ecological studies, good estimates often could not be obtained without imposing constraints upon the estimation procedure, even when the number of age classes in the population was known. If the number of age classes was not known, it was frequently difficult to determine from small samples. When unconstrained solutions were obtainable, confidence limits about estimates were often very wide. Our results and information in the theoretical literature indicate that if the Petersen method (whereby several modes on a size-frequency histogram are taken to represent single age classes and all age classes to be present) does not work, accurate estimates of demographic parameters are unlikely to be obtainable using more rigorous methods. In view of these difficulties, we recommend that an iptimization method, such as that described by Macdonald and Pitcher, be used to estimate demographic parameters. Standard errors of estimates should be reported. Optimization methods give an indication when the data is inadequate to obtain accurate parameter estimates, either by failing to converge or by placing large standard errors about the estimates. Graphical methods do not give a clear warning of this, and should be avoided except where the modes on the size-frequency histogram are very well separated and sample sizes are large. Often, assumptions must be made about population parameters to enable their estimation. This may involve constraining some parameters to particular values, assuming a fixed relationship between cohort mean sizes and their standard deviations, or by assuming that individuals grow according to a von Bertalanffy curve. Any such assumptions need detailed justification in each case.     

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.     

Characterization of soil erosion and its implication to forest management

Forests have traditionally been managed to maximize timber production or economic profit, completely neglecting other forest values. Nowadays, however, forests are being managed for multiple uses. The basic requirement of multiple use forestry is to identify and quantify forest values and to determine management objectives. The priorities of management objectives, however, must be decided. In this study, a model predicting the soil loss for multi objective forest management was developed. The model was based on data from remeasurement of permanent sample plots. The data were gathered from 132 sample plots. Approximately 80% of the observations were used for model development and 20% for validation. The model was designed for even aged and uneven aged forests, as well as for forests with mixed and pure species composition. The explicatory variables in the model were mean diameter and number of trees. All parameter estimates were found highly significant (p < 0.001) in predicting soil loss. The model fit and validation tests were fairly good. The soil loss model presented in this paper was considered to have an appropriate level of reliability. It can be used in the overall multi-objective forest management planning, but, it should be limited to the conditions for which the data were gathered.     

Improved sample preparation and GC–MS analysis of priority organic pollutants

Mass spectrometry is a major tool for analysing organic pollutants. However, scientists often complain about laborious sample preparation. The development of new commercial high-resolution mass spectrometers gives a chance to improve simultaneously speed, reliability, and sensitivity of the analysis. Here, we used the time-of-flight high-resolution mass spectrometer Pegasus GC-HRT to identify and quantify 55 priority organic pollutants in water samples. This mass spectrometer has a high resolution of 50,000, a high mass accuracy of about 1 ppm and a very high acquisition rate of up to 200 full mass range spectra per second. 1 mL water samples were extracted with 1 mL dichloromethane. Results show that the sample preparation and analysis are achieved 30 times faster, requiring 1,000 times less water and 350 times less solvent than the classic 8270 method of the United States Environmental Protection Agency. The detection limit is 1 μg/L. The quantification limit is 10 μg/L. Our procedure, named accelerated water sample preparation, is simpler, faster, cheaper, safer and more reliable than 8270 Method.     

Do echolocation calls of wild colony-living Bechstein's bats (Myotis bechsteinii) provide individual-specific signatures?

Social animals often use vocal communication signals that contain individual signatures. As bats emit echolocation calls several times per second to orient in space, these might seem ideal candidates for conveying the caller's individual identity as a free by-product. From a proximate perspective, however, coding of caller identity is hampered by the simple acoustic structure of echolocation signals, by their task-specific design and by propagation loss. We investigated the occurrence of individual signatures in echolocation calls in individually marked, free-living Bechstein's bats (Myotis bechsteinii) in a situation with defined social context in the field. The bats belonged to two different colonies, for both of which genetic data on relatedness structure was available. While our data clearly demonstrate situation specificity of call structure, the evidence for individual-specific signatures was relatively weak. We could not identify a robust and simple parameter that would convey the caller's identity despite the situation-specific call variability. Discriminant function analysis assigned calls to call sequences with good performance, but worsened drastically when tested with other sequences from the same bats. Therefore, we caution against concluding from a satisfactory discrimination performance with identical training and test sequences that individual bats can reliably be told apart by echolocation calls. At least the information contained in a single call sequence seems not to be sufficient for that purpose. Starting frequencies did give the best discrimination between individuals, and it was also this parameter that was correlated with genetic relatedness in one of our two study colonies. Echolocation calls could serve as an additional source of information for individual recognition in Bechstein's bats societies, while it is unlikely that a large number of individuals could be reliably identified in different situations based on echolocation alone.     

Adenosine nucleotide “energy charge” ratios as an ecophysiological index for microplankton communities

Energy charge (EC) ratios of microplankton samples have been measured from their adenosine triphosphate (ATP), adenosine diphosphate (ADP) and adenosine monophosphate (AMP) contents, according to a method based on enzymatic tranformations of ADP and AMP into ATP, and the subsequent quantitative analysis of the latter by the bioluminescent reaction of a firefly lantern extract (Photinus pyralis). Interference caused by other non-adenylic nucleotides and bioluminescence inhibition by various compounds were reduced, or estimated, by the use of internal standards for each sample. This was accomplished both by the injection of a small volume of a non-commercial extract of P. pyralis and by measurement of the bioluminescent flash at its maximal value. This standard method for preparation and analysis afforded good reproducibility and permitted the calibration of individual samples, thus allowing the comparison and treatment of data in the large series necessary in oceanographic studies. Studies were made on natural populations taken from a polluted marine area where phytoplankton communities live under the stressful influence of an urban sewer outlet, near Marseille (France). Three sampling strategies in surface waters (transects from the outlet, sampling during a 24-h buoydrift, and regular sampling for a day-night period) conducted at a point in front of the outlet revealed a decrease of EC in relation to urban activity or approaching proximity of the sewer outlet. These low EC values (0.2 to 0.5) were caused by a high AMP content, perhaps originating from degraded biogenic particles and dead or metabolically impeded bacteria of terrestrial orgin stressed by ecologic factors such as increased salinity and decreased temperature. Further away from the sewage outlet, the EC increased as the bacterial population decreased, and the phytoplanktonic communities reappeared parallel to the dilution of the effluent. Although in mature and unperturbed ecosystems EC values of 0.70 to 0.80 were recorded, the values were generally lower than those measured in growing bacterial or phytoplankton cultures. This fact may be related to differences in the various metabolic states of multispecific populations. Some EC measurements from deeper microplankton samples presented in this paper were difficult to interpret, reflecting perhaps unsolved problems concerning the treatment of samples. However, it was possible to associate the range of variation in EC values to differences in composition and structure of the ecosystem of microplankton populations in neritic surface waters.     

Estimating prevalence using composites

We are interested in estimating the fraction of a population that possesses a certain trait, such as the presence of a chemical contaminant in a lake. A composite sample drawn from a population has the trait in question whenever one or more of the individual samples making up the composite has the trait. Let the true fraction of the population that is contaminated be p. Classical estimators of p, such as the MLE and the jackknife, have been shown to be biased. In this study, we introduce a new shrinking estimator which can be used when doing composite sampling. The properties of this estimator are investigated and compared with those of the MLE and the jackknife.     

Distribution-free ranked-set sample procedures for umbrella alternatives in the m-sample setting

In settings where measurements are costly and/or difficult to obtain but ranking of the potential sample data is relatively easy and reliable, the use of statistical methods based on a ranked-set sampling approach can lead to substantial improvement over analogous methods associated with simple random samples. Previous nonparametric work in this area has been concentrated almost exclusively on the one- and two-sample location problems. In this paper we develop ranked-set sample procedures for the m-sample location setting where the treatment effect parameters follow a restricted umbrella pattern. Distribution-free testing procedures are developed for both the case where the peak of the umbrella is known and for the case where it is unknown. Small sample and asymptotic null distribution properties are provided for the peak-known test statistic.