Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty.

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naïve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naïve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Spectral Discrimination of Macronutrient Deficiencies in Greenhouse Grown Flue-Cured Tobacco.

Remote sensing of nutrient disorders has become more common in recent years. Most research has considered one or two nutrient disorders and few studies have sought to distinguish among multiple macronutrient deficiencies. This study was conducted to provide a baseline spectral characterization of macronutrient deficiencies in flue-cured tobacco (Nicotiana tabacum L.). Reflectance measurements were obtained from greenhouse-grown nutrient-deficient plants at several stages of development. Feature selection methods including information entropy and first and second derivatives were used to identify wavelengths useful for discriminating among these deficiencies. Detected variability was primarily within wavelengths in the visible spectrum, while near-infrared and shortwave-infrared radiation contributed little to the observed variability. Principal component analysis was used to reduce data dimensionality and the selected components were used to develop linear discriminant analysis models to classify the symptoms. Classification models for young, intermediate, and mature plants had overall accuracies of 92%, 82%, and 75%, respectively, when using 10 principal components. Nitrogen, sulfur, and magnesium deficiencies exhibited greater classification accuracies, while phosphorus and potassium deficiencies demonstrated poor or inconsistent results. This study demonstrates that spectral analysis of flue-cured tobacco is a promising methodology to improve current scouting methods.

Censoring Trace-Level Environmental Data: Statistical Analysis Considerations to Limit Bias.

Trace-level environmental data typically include values near or below detection and quantitation thresholds where health effects may result from low-concentration exposures to one chemical over time or to multiple chemicals. In a cook stove case study, bias in dibenzo[a,h]anthracene concentration means and standard deviations (SDs) was assessed following censoring at thresholds for selected analysis approaches: substituting threshold/2, maximum likelihood estimation, robust regression on order statistics, Kaplan-Meier, and omitting censored observations. Means and SDs for gas chromatography-mass spectrometry-determined concentrations were calculated after censoring at detection and calibration thresholds, 17% and 55% of the data, respectively. Threshold/2 substitution was the least biased. Measurement values were subsequently simulated from two log-normal distributions at two sample sizes. Means and SDs were calculated for 30%, 50%, and 80% censoring levels and compared to known distribution counterparts. Simulation results illustrated (1) threshold/2 substitution to be inferior to modern after-censoring statistical approaches and (2) all after-censoring approaches to be inferior to including all measurement data in analysis. Additionally, differences in stove-specific group means were tested for uncensored samples and after censoring. Group differences of means tests varied depending on censoring and distributional decisions. Investigators should guard against censoring-related bias from (explicit or implicit) distributional and analysis approach decisions.

Spatial Signal Detection Using Continuous Shrinkage Priors.

Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. We apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.