Use of post-stratification in composite sampling for estimating mean

We show with the results of a study conducted in the Hamadan Province, Iran as to how the use of composite sampling for estimating mean zinc concentration in the soil can help reduce analytical costs by reducing the number of analysis required. We also introduce post-stratification methodology in the composition step to take advantage of possible spatial dispersion. We speculate that the zinc concentration value depends on the sample location, we first stratified the sample set and then composite units from different strata randomly. The results of a simulation study show that the use of this approach not only reduces the total costs but also increases the precision of the estimator.     

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.     

Cost analysis of composite sampling for classification

When an environmental sampling objective is to classify all the sample units as contaminated or not, composite sampling with selective retesting can substantially reduce costs by reducing the number of units that require direct analysis. The tradeoff, however, is increased complexity that has its own hidden costs. For this reason, we propose a model for assessing the relative cost, expressed as the ratio of total expected cost with compositing to total expected cost without compositing (initial exhaustive testing). Expressions are derived for the following retesting protocols: (i) exhaustive, (ii) sequential and (iii) binary split. The effects of both false positive and false negative rates are also derived and incorporated. The derived expressions of relative cost are illustrated for a range of values for various cost components that reflect typical costs incurred with hazardous waste site monitoring. Results allow those who are designing sampling plans to evaluate if any of these compositing/retesting protocols will be cost effective for particular applications.     

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.     

Optimizing two- and three-stage designs for spatial inventories of natural resources by simulated annealing

This paper reviews design-based estimators for two- and three-stage sampling designs to estimate the mean of finite populations. This theory is then extended to spatial populations with continuous, infinite populations of sampling units at the latter stages. We then assume that the spatial pattern is the result of a spatial stochastic process, so the sampling variance of the estimators can be predicted from the variogram. A realistic cost function is then developed, based on several factors including laboratory analysis, time of fieldwork, and numbers of samples. Simulated annealing is used to find designs with minimum sampling variance for a fixed budget. The theory is illustrated with a real-world problem dealing with the volume of contaminated bed sediments in a network of watercourses. Primary sampling units are watercourses, secondary units are transects perpendicular to the axis of the watercourse, and tertiary units are points. Optimal designs had one point per transect, from one to three transects per watercourse, and the number of watercourses varied depending on the budget. However, if laboratory costs are reduced by grouping all samples within a watercourse into one composite sample, it appeared to be efficient to sample more transects within a watercourse.     

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.     

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.     

Discovery of emerging organic pollutants in the atmosphere through an omics approach

● We review the framework of discovering emerging pollutants through an omics approach. ● High-resolution MS can digitalize atmospheric samples to full-component data. ● Chemical features and databases can help to translate untargeted data to compounds. ● Biological effect-directed untargeted analyses consider both existence and toxicity. Ambient air pollution, containing numerous known and hitherto unknown compounds, is a major risk factor for public health. The discovery of harmful components is the prerequisite for pollution control; however, this raises a great challenge on recognizing previously unknown species. Here we systematically review the analytical techniques on air pollution in the framework of an omics approach, with a brief introduction on sample preparation and analysis, and in more detail, compounds prioritization and identification. Through high-resolution mass spectrometry (HRMS, typically coupled with chromatography), the complicated environmental matrix can be digitalized into “full-component” data. A key step to discover emerging compounds is the prioritization of compounds from massive data. Chemical fingerprints, suspect lists and biological effects are the most vital untargeted strategies for comprehensively screening critical and hazardous substances. Afterward, compressed data of compounds can be identified at various confidence levels according to exact mass and the derived molecular formula, MS libraries, and authentic standards. Such an omics approach on full-component data provides a paradigm for discovering emerging air pollutants; nonetheless, new technological advancements of instruments and databases are warranted for further tracking the environmental behaviors, hence to evaluate the health risk of key pollutants.     

An Empirical Analysis of Exposure-Based Regulation to Abate Toxic Air Pollution

Title III of the 1990 Clean Air Act Amendments requires the Environmental Protection Agency to regulate 189 air toxics, including emissions from by-product coke ovens. Economists criticize the inefficiency of uniform standards, but Title III makes no provision for flexible regulatory instruments. Environmental health scientists suggest that population exposure, not necessarily ambient air quality, should motivate environmental air pollution policies. Using an engineering-economic model of the United States steel industry, we estimate that an exposure-based policy can achieve the same level of public health as coke oven emissions standards and can reduce compliance costs by up to 60.0%.     

Contributions to composite sampling

The initial use of composite sampling involved the analysis of many negative samples with relatively high laboratory cost (Dorfman sampling). We propose a method of double compositing and compare its efficiency with Dorfman sampling. The variability of composite measurement samples has environmental interest (hot spots). The precision of these estimates depends on the kurtosis of the distribution; leptokurtic distributions (₂ > 0) have increased precision as the number of field samples is increased. The opposite effect is obtained for platykurtic distributions. In the lognormal case, coverage probabilities are reasonable for < 0.5. The Poisson distribution can be associated with temporal compositing, of particular interest where radioactive measurements are taken. Sample size considerations indicate that the total sampling effort is directly proportional to the length of time sampled. If there is background radiation then increasing levels of this radiation require larger sample sizes to detect the same difference in radiation.     

Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.     

Assessment of the environmental conditions of the Sarno river basin (south Italy): a stream sediment approach

The Sarno river basin covers an area of 500 km² collecting the waters of Solofrana and Cavaiola tributaries. Originally it manly represents a source of livelihood for inhabitants by fishing and transporting goods; currently, the Sarno river, still partially used for irrigation, is affected by an extreme environmental degradation as a result of uncontrolled outflow of industrial waste. Within the framework of a wider geochemical prospecting project aiming at characterizing the whole territory of the Campania region, 89 stream sediment samples with a sampling density of 1 sample per 5 km² were collected in the river basin and analyzed by means of inductively coupled plasma-mass spectrometry in order to assess the environmental conditions at a regional scale. A GIS-aided technique, based on both the actual distribution of potentially harmful elements and their regional background values, was used to generate the maps of the contamination factors and of the contamination degrees for As, Cd, Cr, Cu, Hg, Pb and Zn. Furthermore, a factor analysis was performed to assess the nature and the extent of contamination sources for the river sediments. Results showed that the Sarno river basin could be divided in two “environmental status” units: one, low contaminated, corresponding to the hilly and mountain areas, and the second, from moderately to very highly contaminated, corresponding to the economically developed areas of the valley floor characterized by a high population density. This work was developed within a project that aims to investigate the relationships between environmental pollution and human health by analyzing environmental media (stream sediments, water, soil and vegetation) together with human hair of resident population. In this context, the spatial correlation between the extremely compromised environmental conditions of developed areas and the incidence rate of liver cancer in the same area was also explored posing the need of a careful costs/benefits analysis to assess whether the deterioration of the environment, that could adversely affect the conditions of public health, is worth the economic development.     

Interdisciplinarity and participatory approaches to environmental health

This paper reviews a workshop discussion postulated on the notion that social, economic and behavioural factors are responsible for the creation of environmental hazards and benefits that, in turn, can affect human health, with concomitant effects on future social well-being. The workshop case study centred on environmental health investigations, public engagement and partnership work undertaken following the death of two neighbouring children in Cheshire. Discussion included questions of causality and generalisability. It revealed how the attribution of responsibility for environmental damage to health is fraught with difficulties. It may often militate against an informed and open debate among interested parties, with concomitant implications for reducing the danger from environmental hazards. To improve communication, vocabulary needs to be free from jargon and acronyms, and differences in conceptual approach between different disciplines need to be better understood. The definition of the ‘community’ is itself far from clear-cut, yet questions of how to involve this community in intervention processes are important ones. The workshop identified a clear need for better, more considered forms of communication with communities and the public if fears are to be allayed, but recognised the additional costs that this would incur.     

Efficiency of composite sampling for estimating a lognormal distribution

In many environmental studies measuring the amount of a contaminant in a sampling unit is expensive. In such cases, composite sampling is often used to reduce data collection cost. However, composite sampling is known to be beneficial for estimating the mean of a population, but not necessarily for estimating the variance or other parameters. As some applications, for example, Monte Carlo risk assessment, require an estimate of the entire distribution, and as the lognormal model is commonly used in environmental risk assessment, in this paper we investigate efficiency of composite sampling for estimating a lognormal distribution. In particular, we examine the magnitude of savings in the number of measurements over simple random sampling, and the nature of its dependence on composite size and the parameters of the distribution utilizing simulation and asymptotic calculations.     

Altruism and environmental risks to health of parents and their children

This paper tests an equilibrium condition from a model that incorporates: (1) altruism of parents toward their young children, and (2) household production of latent health risks. The model demonstrates that an altruistic parent's marginal rate of substitution between an environmental health risk to herself and to her child is equal to the ratio of marginal risk reduction costs. Econometric estimates support this prediction based on data from a stated preference survey involving 488 parents of children aged 3–12 years. This outcome implies that parents reallocate family resources to at least partly offset the effectiveness of public programs that aim to reduce their children's environmental risks.     

Ranked set sample design for environmental investigations

Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions     

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.     

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.     

Precision of the mean and the design of benthos sampling programmes: caution revised

Normative variance functions can be used to accurately predict sampling exigencies, but such empirically derived formulae are continuous functions that can predict levels of sampling precision that cannot logically occur in discrete population samples. General formulae are presented that allow calculation of upper and lower boundary constraints on levels of sampling precision. These boundary constraints would only have a significant influence on sampling design where populations are so sparse that samples consist mainly of presence-absence data. A previously published empirical equation for the prediction of requisite sample number for the estimation of a freshwater benthos population correctly shows that using a small sampler can result in an up to 50-fold reduction in the amount of sediment processed, regardless of these constraints. A previously published empirical equation for the prediction of sampling variance, based on over 3000 sets of replicate samples of marine benthos populations, suggests that the use of small samplers over large ones requires the processing of between one-half and one-twentieth of the sediment for the same level of precision. It is concluded that discussions of sampling optimization should be based on knowledge of real sampling costs.     

Biomonitoring mit Stadttaubeneiern

Experiences of biological monitoring with feral pigeons over a 12-year period in the cities of Halle, leipzig and Saarbrücken, and in rural areas of the Saarland and Schleswig-Holstein, show how to combine the management of feral pigeon populations with scientific questions. Especially the eggs of feral pigeons are suitable for environmental observation. Their advantage is, to show both concentrations of substances and their effects. In addition, there is almost no alternative in urban ecosystems by the use of other specimens. Requirements on standard operation procedures for sampling and sample treatment are presented. Examples of significant differences in analytical and biometric information between the observed areas and trends over the 12-year monitoring period with the use of pigeon eggs are presented. In specially constructed pigeon houses (pigeonry) with nesting cells, pigeon eggs can permanently be used for long term monitoring studies. At the same time, the possibility for the control and regulation of population health and desity is given.