Revisiting Pierre Gy's formula (TOS) - A return to size-density classes for applications to contaminated soils, coated particular aggregates and mixed material systems.

For some real-world material systems, estimations of the incompressible sampling variance based on Gy's classical s(FSE) formula from the Theory of Sampling (TOS) show a significant discrepancy with empirical estimates of sampling variance. In instances concerning contaminated soils, coated particular aggregates and mixed material systems, theoretical estimates of sampling variance are larger than empirical estimates, a situation which does not have physical meaning in TOS. This has led us to revisit the development of estimates of s(FSE) from this famous constitutional heterogeneity equation and explore the use of size-density classes for mixed material systems (mixtures of both analyte-enriched and coated particles), an approach which has been mostly unused since Gy's original derivation.

Sampling particulate matter for analysis - Controlling uncertainty and bias using the theory of sampling.

Sampling particulate matter for measuring the content of an analyte is a routine operation in many fields of engineering and science. However, sampling can lead to important bias and variance in concentration estimation because of sampling errors stemming from particulate matter heterogeneity. The goal of this study was to quantify bias, reproducibility and the degree of representativeness of a probabilistic sampling (PS) technique following principles from the Theory of sampling (TOS) and grab sampling (GS).

Toward improved analysis of concentration data: Embracing nondetects.

Various statistical tests on concentration data serve to support decision-making regarding characterization and monitoring of contaminated media, assessing exposure to a chemical, and quantifying the associated risks. However, the routine statistical protocols cannot be directly applied because of challenges arising from nondetects or left-censored observations, which are concentration measurements below the detection limit of measuring instruments. Despite the existence of techniques based on survival analysis that can adjust for nondetects, these are seldom taken into account properly.

Application of mixed effects models for characterizing contaminated sites.

In a typical data collection process for the purpose of characterizing contaminated sites, boreholes are usually drilled in different locations based on a sampling plan; and consequently, multiple samples are collected from each borehole. As a result, it is quite plausible that a certain degree of dependency or similarity exists among observations nested within a borehole. However, when classical regression models are employed, such dependencies are often ignored, resulting in biased estimates.

An investigation of the impact of left-censored soil contamination data on the uncertainty of descriptive statistical parameters.

Left-censored concentration data are frequently encountered because measuring instruments cannot detect concentrations below the instrument detection limit. For statistical analysis of left-censored data, the environmental literature mainly refers to the following methods: maximum likelihood estimator, regression on order statistics using log-normal and gamma assumption (rROS and GROS, respectively), and Kaplan-Meier. A number of simulation experiments examined the performance of these methods in terms of bias and/or mean square error.

Estimating the mean and standard deviation of environmental data with below detection limit observations: Considering highly skewed data and model misspecification.

In environmental studies, concentration measurements frequently fall below detection limits of measuring instruments, resulting in left-censored data. Some studies employ parametric methods such as the maximum likelihood estimator (MLE), robust regression on order statistic (rROS), and gamma regression on order statistic (GROS), while others suggest a non-parametric approach, the Kaplan-Meier method (KM). Using examples of real data from a soil characterization study in Montreal, we highlight the need for additional investigations that aim at unifying the existing literature.

Representativeness of laboratory sampling procedures for the analysis of trace metals in soil.

This study was conducted to assess the representativeness of laboratory sampling protocols for purposes of trace metal analysis in soil. Five laboratory protocols were compared, including conventional grab sampling, to assess the influence of sectorial splitting, sieving, and grinding on measured trace metal concentrations and their variability. It was concluded that grinding was the most important factor in controlling the variability of trace metal concentrations.

Analysis of procedures for sampling contaminated soil using Gy's Sampling Theory and Practice.

Soil sampling is a critical step in environmental site assessment studies. The representativeness of soil samples has a direct influence on financial, liability, environmental and public health issues associated with the outcome of remediation activities. Representativeness must be quantified for assessing and designing soil sampling procedures.