Richard O. Gilbert

Statistical Methods for Estimating the Mean and Variance from Radionuclide Data Sets Containing Negative, Unreported Or Less-than Values

AbstractThis paper reviews statistical procedures for estimating the mean μ, and standard deviation (S.D.) sigma of radionuclide data sets containing negative, unreported, or “less-than” values resulting from concentrations being less than the analytical detection limit. Computational precedures lea

Kriging for estimating spatial pattern of contaminants: potential and problems

This paper discusses and illustrates the use of kriging techniques for estimating the spatial pattern of contaminants in environmental media, particularly soil. The assumptions underlying kriging are reviewed as are some advantages and disadvantages of the method. Lognormal kriging (kriging applied to logarithmic-transformed data) is illustrated using a set of radionuclide soil concentrations at a nuclear testing area on the Nevada Test Site. This example shows how lognormal kriging can be used to estimate average concentrations at points or for blocks of land, concentration contours over space, confidence bands about these contours, and radionuclide inventory in soil. The validity of kriging estimates depends on the accurate estimation and modeling of the spatial correlation structure of the phenomenon. Accuracy is especially important when lognormal kriging is used and estimates of means and their standard deviations are required in the original, untransformed scale. This paper illustrates the bias that can result when a changing correlation structure over space is ignored.

Transfer of Aged Pu to Cattle Grazing on a Contaminated Environment

Estimates are obtained of the fraction of ingested or inhaled 239+240Pu transferred to blood and tissues of a reproducing herd of beef cattle, individuals of which grazed within fenced enclosures for up to 1064 d under natural conditions with no supplemental feeding at an arid site contaminated 16 y previously with Pu oxide. The estimated (geometric mean [GM]) fraction of Pu transferred from the gastrointestinal tract to blood serum was about 5 x 10(-6) (geometric standard error [GSE] = 1.4) with an approximate upper bound of about 2 x 10(-5). These results are in reasonable agreement with the value of 1 x 10(-5) recommended for human radiation protection purposes by the International Commission on Radiological Protection (ICRP) for insoluble Pu oxides that are free of very small particles. Also, results from a laboratory study by Stanley (St75), in which large doses of 238Pu were orally administered daily to dairy cattle for 19 consecutive days, suggest that aged 239+240Pu at this arid grazing site may not be more biologically available to blood serum than fresh 239+240Pu oxide. The estimated fractions of 239+240Pu transferred from blood serum to tissues of adult grazing cattle were: femur (3.2 X 10(-2), 1.8; GM, GSE), vertebra (1.4 X 10(-1), 1.6), liver (2.3 X 10(-1), 2.0), muscle (1.3 X 10(-1), 1.9), female gonads (7.9 X 10(-5), 1.5), and kidney (1.4 X 10(-3), 1.7). The blood-to-tissue fractional transfers for cattle initially exposed in utero were greater than those exposed only as adults by a factor of about 4 for femur (statistically significant) and of about 2 for other tissues (not significant). The estimated (GM) fraction of inhaled Pu initially deposited in the pulmonary lung was 0.34 (GSE = 1.3) for adults and 0.15 (GSE = 1.3) for cattle initially exposed in utero (a statistically significant difference), which may be compared with the expected fraction of 0.11 at the study site using the ICRP lung model for humans.

Role of Sampling Designs in Obtaining Representative Data

Representative environmental data are necessary to make defensible environmental decisions. Representative data can be obtained using unbiased sampling designs developed in the context of the project to achieve sampling objectives with required confidence and minimal cost. This article stresses the importance of systematic planning and an adequate conceptual site model to develop an appropriate sampling design. Various sampling designs are discussed and examples are used to illustrate sampling designs for various sampling objectives.

Transfer of aged 239+240Pu, 238Pu, 241Am, and 137Cs to cattle grazing a contaminated arid environment

In this paper, estimates are obtained of the fraction of ingested 239+240Pu, 238Pu, 241Am and 137Cs transferred to blood, muscle, liver, kidney, femur, vertebra, and gonads of a reproducing herd of 17 beef cattle, individuals of which grazed within fenced enclosures for up to 1064 days under natural conditions with no supplemental feeding at an arid site contaminated 16 years previously with transuranic radionuclides. The estimated geometric mean (GM) GI-to-blood fractional transfer of 238Pu (0.0001) was about 20 times larger than the estimated transfer of 239+240Pu (0.000005), while the estimated transfer of 241Am (0.00001) was about 2 times larger than that of 239+240Pu. These GM GI-to-blood transfers were smaller than the GI-to-blood transfer value of 0.001 recommended by the International Commission on Radiological Protection (ICRP) for humans exposed via food chains or occupationally from unknown mixtures or compounds of plutonium and americium. Statistical tests indicated significantly (p less than 0.05) larger GI-to-tissue transfers of (1) 238Pu as compared to 239+240Pu for all tissues examined, (2) of 238Pu as compared to 241Am for muscle, liver, femur, and vertebra, and (3) of 241Am as compared to 239+240Pu for blood serum, femur, and kidney. The estimated GM fractional transfers of 137Cs from GI to muscle and liver were 0.03 (n = 8) and 0.001 (n = 3), respectively, assuming a 50-day biological half-time of 137Cs in cattle tissue.

Comparing computing formulas for estimating concentration ratios

Abstract The purpose of this paper is to provide guidance on the choice of computing formulas (estimators) for estimating average concentration ratios and other ratio-type measures of radionuclides and other environmental contaminant transfers between ecosystem components. Mathematical expressions for the expected value of three commonly used estimators (arithmetic mean of ratios, geometric mean of ratios, and the ratio of means) are obtained when the multivariate lognormal distribution is assumed. These expressions are used to explain why these estimators will not in general give the same estimate of the average concentration ratio. They illustrate that the magnitude of the discrepancies depends on the magnitude of measurement biases, and on the variance and correlations associated with spatial heterogeneity and measurement errors. This paper also reports on a computer simulation study that compares the accuracy of eight computing formulas for estimating a ratio relationship that is constant over time and/or space. Statistical models appropriate for both controlled spiking experiments and observational field studies for either normal or lognormal distributions are considered. Our results indicate that for either type of study the geometric mean is generally preferred if the lognormal distribution applies. However, the geometric mean has the disadvantage that its expected value depends on n , the number of measurements taken. Rickers estimator, R rt , appears to perform worse than the other estimators studied when the observations are lognormal. All eight estimators appear to be equally accurate for the controlled spiking study when data are normally distributed. For observational field studies when data are normally distributed the ratio of means or slight modifications thereof are preferred to other estimators investigated. Before one chooses a computing formula for estimating a concentration ratio, thought should be given to what target value needs to be estimated to satisfy study objectives, and to whether the normal or lognormal distribution is a more realistic model. The geometric mean performs well for lognormal distributions, but comparison of geometric means or of a geometric mean with environmental limits can be misleading if n is small. The arithmetic mean of ratios is a conservative choice in that it will always give a larger estimate than will the geometric mean. It may also be severely biased when data are lognormal and the variances of measurement errors are large. The ratio of the means is a reasonable choice if the distribution is normal. The median of the observed ratios, R md , is useful estimate since it is easily obtained and has an easily understood interpretation as the point above which and below which 50% of the observed ratios lie. Also, it is appropriate no matter what the distribution of the observed ratios may be. Confidence limits on the median are also easily obtained. Finally, while this paper emphasizes applications in radionuclide research, our results should be applicable to a wide range of environmental contaminants since many contaminants have approximately lognormal distributions.

Determining the optimum number of increments in composite sampling

Composite sampling can be more cost effective than simple random sampling. This paper considers how to determine the optimum number of increments to use in composite sampling. Composite sampling terminology and theory are outlined and a method is developed which accounts for different sources of variation in compositing and data analysis. This method is used to define and understand the process of determining the optimum number of increments that should be used in forming a composite. The blending variance is shown to have a smaller range of possible values than previously reported when estimating the number of increments in a composite sample. Accounting for differing levels of the blending variance significantly affects the estimated number of increments.

A Monte Carlo Study of Analysis of Variance and Competing Rank Tests for Scheffé's Mixed Model

Abstract Monte Carlo estimates are obtained of the small sample power of the classical F test and three competing rank tests for detecting two forms of treatment shift alternatives. These results were computed under Scheffes mixed model for the case of one observation per cell using several variance-covariance matrices. Some small sample null distributions, empirical efficiencies, and robustness computations are also given.

Version 2.0 Visual Sample Plan (VSP): Models and Code Verification

Visual Sample Plan (VSP) is an easy-to-use visual and graphic software tool being developed by the Pacific Northwest National Laboratory (PNNL) to select the right number and location of environmental samples so that the results of statistical tests performed to provide input to environmental decisions have the required confidence and performance. It is a significant help in implementing the Data Quality Objectives (DQO) planning process that was developed by the U. S. Environmental Protection Agency. Gilbert et al. (2001) documented the quality assurance (QA) procedures that were conducted to assure that Version 0.91 of VSP was operating correctly. Subsequently, Version 0.91 was renamed Version 1.0 and placed on the internet at http://dqo.pnl.gov/vsp . Since that time VSP has been enlarged and improved and is now available as Version 2.0. The current document is an expansion of Gilbert et al (2001) to include the QA procedures and testing that were conducted to assure the validity and accuracy of the new features added to Version 1.0 to obtain Version 2.0.

Statistical Methods and Tools for Uxo Characterization (SERDP Final Technical Report)

The Strategic Environmental Research and Development Program (SERDP) issued a statement of need for FY01 titled Statistical Sampling for Unexploded Ordnance (UXO) Site Characterization that solicited proposals to develop statistically valid sampling protocols for cost-effective, practical, and reliable investigation of sites contaminated with UXO; protocols that could be validated through subsequent field demonstrations. The SERDP goal was the development of a sampling strategy for which a fraction of the site is initially surveyed by geophysical detectors to confidently identify clean areas and subsections (target areas, TAs) that had elevated densities of anomalous geophysical detector readings that could indicate the presence of UXO. More detailed surveys could then be conducted to search the identified TAs for UXO. SERDP funded three projects: those proposed by the Pacific Northwest National Laboratory (PNNL) (SERDP Project No. UXO 1199), Sandia National Laboratory (SNL), and Oak Ridge National Laboratory (ORNL). The projects were closely coordinated to minimize duplication of effort and facilitate use of shared algorithms where feasible. This final report for PNNL Project 1199 describes the methods developed by PNNL to address SERDPs statement-of-need for the development of statistically-based geophysical survey methods for sites where 100% surveys are unattainable or cost prohibitive.