Estimating Trophic State Proportions of a Regional Lake Population: Are Larger Samples Always Better?

During the summers of 1991–1994, the Environmental Monitoringand Assessment Program (EMAP) sampled 344 lakes throughout thenortheastern United States using a proportional stratified sampling design based on lake size. Approximately one-quarter ofthe 344 lakes were sampled each year (4 years) for totalphosphorus to determine the proportion (and associated95% confidence intervals) of the northeast lake population 1ha (11,076 ± 1,699 lakes) that was in oligotrophic,mesotrophic, eutrophic, or heupereutropic (4 classes) conditionaccording to the total phosphorus criteria of the North AmericaLake Manegement Society. Estimates for the second, third, andfourth yr were developed as cumulative of the previous yrsamples and the current yr samples for the northeast as a wholeand for each of its three ecoregions (4 regions). New confidence intervals were computed for each cumulative yrcondition estimate. This produced a total (4 years × 4classes × 4 regions) of 64 cumulative yr tropic conditionestimates. Confidence intervals for 21% of these estimates didnot shorten with increased sample size. This phenomena raisedquestions about the accuracy of estimates based on cumulativesampling procedures. We explain why and how the phenomenon comesabout with both straight random and proportional randomsampling. Further, we present an example of the effects thisphenomenon has on lake tropic state condition estimates in thenortheastern United States.     

Methods of Assessing and Achieving Normality Applied to Environmental Data

2 and particle concentrations. Results show that the analyzed transformations work well and are very useful to achieve normal distributions.     

燃煤电厂大气污染物排放考核时间间隔的建议

新的《火电厂大气污染物排放标准》和新《环境保护法》实施后,燃煤火电企业的依法治企自觉性不断提高,但由于不同的环保管理文件对超标处罚依据和处罚手段不同,造成政府对企业处罚的自由裁量权加大,对企业造成一定的压力与困惑。结合企业实际运行情况对燃煤电厂大气污染物排放考核时间间隔提出建议。     

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS1

ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.     

Use of Approximate Inference in an Index of Completeness of Biological Inventories

Abstract:  To assess the completeness of a floristic or faunal inventory, one may use the ratio of the observed number of species to the "true number" of species ( C ). If the inventory is complete , C = 1. The estimate of the true number can be obtained from accumulation curves, nonparametric methods, or other techniques. We devised a simple method for computing confidence intervals (CI) for C and for evaluating the null hypothesis that the inventory is complete. The method is based on the assumptions that an estimate of the variance of the true number of species is known and that the distribution of the estimator of the true number of species is approximately normal. We applied our method to bird inventories in the Balsas Basin of Mexico. The completeness index for subtransects were lower (84.0, 85.4, and 89.9%) than for the whole transect (91.6%) (all significantly different from 100%). Thus, these particular inventories were incomplete at 2 spatial resolutions. Our method of estimating CI for C can be used to estimate species richness obtained from databases of different sites or to test the null hypothesis that an inventory derived from a database is complete.     

A new baseline model for estimating willingness to pay from discrete choice models

We show a substantive problem exists with the widely-used ratio of coefficients approach to calculating willingness to pay (WTP) from discrete choice models. The correctly calculated standard error for WTP using this approach is shown to be undefined. This occurs because the cost parameter's standard error implies some possibility the true parameter value is arbitrarily close to zero. We propose a simple yet elegant way to overcome this problem by reparameterizing the (negative) cost variable's coefficient using an exponential transformation to enforce the theoretically correct positive coefficient. With it the confidence interval for WTP is now finite and well behaved.     

Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population

Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.     

Empirical Bayes calculations of concordance between endpoints in environmental toxicity experiments

Hierarchical models are considered for estimating the probability of agreement between two outcomes or endpoints from an environmental toxicity experiment. Emphasis is placed on generalized regression models, under which the prior mean is related to a linear combination of explanatory variables via a monotone function. This function defines the scale over which the systematic effects are modelled as additive. Specific illustration is provided for the logistic link function. The hierarchical model employs a conjugate beta prior that leads to parametric empirical Bayes estimators of the individual agreement parameters. An example from environmental carcinogenesis illustrates the methods, with motivation derived from estimation of the concordance between two species carcinogenicity outcomes. Based on a large database of carcinogenicity studies, the inter-species concordance is seen to be reasonably informative, i.e. in the range 67–84%. Stratification into pertinent potency-related sub-groups via the logistic model is seen to improve concordance estimation: for environmental stimuli at the extremes of the potency spectrum, concordance can reach well above 90%.     

Some statistical and conceptual issues in the detection of low-level environmental pollutants

With increasing concern over chemicals that are potential health hazards at low levels, determination of limits of detection have undergone considerable scrutiny. Most traditional detection limit estimators suffer from extensive statistical and/or conceptual limitations. In this paper, traditional detection limit estimators are described and critically evaluated. Using the terminology of Currie (1968), methods are categorized into decision limits versus detection limits. The methods are further categorized into single concentration design versus calibration design methodologies. While the single concentration design methods are useful for fixing ideas and clarifying definitions, they are shown to be extremely limited in practice since dependence of variability on concentration can neither be estimated or incorporated. Calibration-based detection limit estimators are described, compared and contrasted. Generalizations to non-constant variance, multiple future detection decisions and simultaneous control of Type I and II errors are provided. The various calibration-based methods are illustrated using real data and experimental design issues for detection limit studies discussed.