Sample Entropy Statistics and Testing for Order in Complex Physiological Signals

Sample Entropy (SampEn) statistics have provided insight into the amount of order present in several types of complex physiological time series, particularly the heart rate dynamics of premature infants. Very little, however, is known of SampEn's statistical properties and this has hindered strategies for optimization and significance testing. This article shows that SampEn statistics are asymptotically Gaussian under general conditions. A straightforward point estimate of the statistic's variance is developed and compared to empirical results obtained from complex surrogate data. Statistical tests are developed to quantify the amount and scale of order detected in a signal. These tests are used to show that significant order is, in fact, being detected in the heart rate dynamics of neonates, and to suggest strategies for optimizing the analysis parameters.     

Infants' discrimination of consonant contrasts in the presence and absence of talker variability

To learn speech-sound categories, infants must identify the acoustic dimensions that differentiate categories and selectively attend to them as opposed to irrelevant dimensions. Variability on irrelevant acoustic dimensions can aid formation of robust categories in infants through adults in tasks such as word learning (e.g., Rost and McMurray, 2009) or speech-sound learning (e.g., Lively et al., 1993). At the same time, variability sometimes overwhelms learners, interfering with learning and processing. Two prior studies (Kuhl & Miller, 1982; Jusczyk, Pisoni, & Mullennix, 1992) found that irrelevant variability sometimes impaired early sound discrimination. We asked whether variability would impair or facilitate discrimination for older infants, comparing 7.5-month-old infants' discrimination of an early acquired native contrast, /p/ vs. /b/ (in the word forms /pIm/ vs. /bIm/), in Experiment 1, with an acoustically subtle, non-native contrast, /n/ vs. /ŋ/ (in /nIm/ vs. /ŋIm/), in Experiment 2. Words were spoken by one or four talkers. Infants discriminated the native but not the non-native contrast, and there were no significant effects of talker condition. We discuss implications for theories of phonological learning and avenues for future research.     

Waste Package Performance Evaluations for the Proposed High-Level Nuclear Waste Repository at Yucca Mountain

The evaluation studies of the proposed repository for long-term storage of spent nuclear fuel and high-level nuclear waste at Yucca Mountain, Nevada, are underway. Fulfillment of the requirements for limiting dose to the public, which includes containment of the radioactive waste emplaced in the proposed repository and subsequent slow release of radionuclides from the Engineered Barrier System (EBS) into the geosphere, will rely on a robust waste container design, among other EBS components. Part of the evaluation process involves sensitivity studies aimed at elucidating which model parameters contribute most to the waste package and overlying drip shield degradation characteristics. The model parameters identified for this study include (1) general corrosion rate parameters and (2) stress corrosion cracking (SCC) parameters. Temperature dependence and parameter uncertainty are evaluated for the general corrosion rate model parameters while for the SCC model parameters, uncertainty treatment of stress intensity factor, crack initiation threshold, and manufacturing flaw orientations are evaluated. Based on these evaluations new uncertainty distributions are generated and recommended for future analyses. Also, early waste package failures due to improper heat treatment were added to the waste package degradation model. The results of these investigations indicate that the waste package failure profiles are governed by the manufacturing flaw orientation model parameters.     

Differences in Pharmacokinetics Between Children and Adults—II. Children''s Variability in Drug Elimination Half-Lives and in Some Parameters Needed for Physiologically-Based Pharmacokinetic Modeling

In earlier work we assembled a database of classical pharmacokinetic parameters (e.g., elimination half-lives; volumes of distribution) in children and adults. These data were then analyzed to define mean differences between adults and children of various age groups. In this article, we first analyze the variability in half-life observations where individual data exist. The major findings are as follows. The age groups defined in the earlier analysis of arithmetic mean data (0-1 week premature; 0-1 week full term; 1 week to 2 months; 2-6 months; 6 months to 2 years; 2-12 years; and 12-18 years) are reasonable for depicting child/adult pharmacokinetic differences, but data for some of the earliest age groups are highly variable. The fraction of individual children's half-lives observed to exceed the adult mean half-life by more than the 3.2-fold uncertainty factor commonly attributed to interindividual pharmacokinetic variability is 27% (16/59) for the 0-1 week age group, and 19% (5/26) in the 1 week to 2 month age group, compared to 0/87 for all the other age groups combined between 2 months and 18 years. Children within specific age groups appear to differ from adults with respect to the amount of variability and the form of the distribution of half-lives across the population. The data indicate departure from simple unimodal distributions, particularly in the 1 week to 2 month age group, suggesting that key developmental steps affecting drug removal tend to occur in that period. Finally, in preparation for age-dependent physiologically-based pharmacokinetic modeling, nationally representative NHANES III data are analyzed for distributions of body size and fat content. The data from about age 3 to age 10 reveal important departures from simple unimodal distributional forms-in the direction suggesting a subpopulation of children that are markedly heavier than those in the major mode. For risk assessment modeling, this means that analysts will need to consider "mixed" distributions (e.g., two or more normal or log-normal modes) in which the proportions of children falling within the major versus highweight/fat modes in the mixture changes as a function of age. Biologically, the most natural interpretation of this is that these subpopulations represent children who have or have not yet received particular signals for change in growth pattern. These apparently distinct subpopulations would be expected to exhibit different disposition of xenobiotics, particularly those that are highly lipophilic and poorly metabolized.     

Quantitative Analysis of Variability and Uncertainty with Known Measurement Error: Methodology and Case Study

The appearance of measurement error in exposure and risk factor data potentially affects any inferences regarding variability and uncertainty because the distribution representing the observed data set deviates from the distribution that represents an error-free data set. A methodology for improving the characterization of variability and uncertainty with known measurement errors in data is demonstrated in this article based on an observed data set, known measurement error, and a measurement-error model. A practical method for constructing an error-free data set is presented and a numerical method based upon bootstrap pairs, incorporating two-dimensional Monte Carlo simulation, is introduced to address uncertainty arising from measurement error in selected statistics. When measurement error is a large source of uncertainty, substantial differences between the distribution representing variability of the observed data set and the distribution representing variability of the error-free data set will occur. Furthermore, the shape and range of the probability bands for uncertainty differ between the observed and error-free data set. Failure to separately characterize contributions from random sampling error and measurement error will lead to bias in the variability and uncertainty estimates. However, a key finding is that total uncertainty in mean can be properly quantified even if measurement and random sampling errors cannot be separated. An empirical case study is used to illustrate the application of the methodology.     

Two simple measures of variability for categorical data

This paper proposes two new variability measures for categorical data. The first variability measure is obtained as one minus the square root of the sum of the squares of the relative frequencies of the different categories. The second measure is obtained by standardizing the first measure. The measures proposed are functions of the variability measure proposed by Gini [Variabilitá e Mutuabilitá Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche, C. Cuppini, Bologna, 1912] and approximate the coefficient of nominal variation introduced by Kvålseth [Coefficients of variation for nominal and ordinal categorical data, Percept. Motor Skills 80 (1995), pp. 843–847] when the number of categories increases. Different mathematical properties of the proposed variability measures are studied and analyzed. Several examples illustrate how the variability measures can be interpreted and used in practice.     

Some characteristics on the selection of spline smoothing parameter

The smoothing spline method is used to fit a curve to a noisy data set, where selection of the smoothing parameter is essential. An adaptive C_p criterion (Chen and Huang 2011 Chen, C. S., and H. C. Huang. 2011. An improved C_p criterion for spline smoothing. Journal of Statistical Planning and Inference 141:445–52.[Crossref], [Web of Science ®] , [Google Scholar]) based on the Stein’s unbiased risk estimate has been proposed to select the smoothing parameter, which not only considers the usual effective degrees of freedom but also takes into account the selection variability. The resulting fitted curve has been shown to be superior and more stable than commonly used selection criteria and possesses the same asymptotic optimality as C_p. In this paper, we further discuss some characteristics on the selection of smoothing parameter, especially for the selection variability.     

Predicting children's internalizing symptoms across development from early emotional reactivity

Current methods of assessing children's emotional reactivity fail to capture individual differences in emotion across contexts that may be meaningfully related to youth psychopathology. We therefore explored the utility of modeling variability in young children's positive and negative emotion across emotionally evocative laboratory tasks to predict later adjustment. At age 3, 409 children completed a battery of laboratory tasks eliciting either positive or negative affect. We used latent difference score (LDS) modeling to predict children's caregiver-reported internalizing symptoms across ages 3, 5, 8, and 11 from variability in their observer-rated positive and negative emotion across laboratory tasks. We found that sex moderated the association between both average and variability measures of children's negative emotion at age 3 and trajectories of their anxious-depressive symptoms across childhood. Measures of emotion variability predicted children's internalizing symptoms above and beyond measures of average emotion. Variability indices also provided unique information about the trajectories of children's symptoms. We discuss implications for the utility of LDS modeling in assessing children's emotional reactivity.     

Parameter Uncertainty and Variability In Evaluative Fate and Exposure Models

The human toxicity potential, a weighting scheme used to evaluate toxic emissions for life cycle assessment and toxics release inventories, is based on potential dose calculations and toxicity factors. This paper evaluates the variance in potential dose calculations that can be attributed to the uncertainty in chemical-specific input parameters as well as the variability in exposure factors and landscape parameters. A knowledge of the uncertainty allows us to assess the robustness of a decision based on the toxicity potential; a knowledge of the sources of uncertainty allows us to focus our resources if we want to reduce the uncertainty. The potential dose of 236 chemicals was assessed. The chemicals were grouped by dominant exposure route, and a Monte Carlo analysis was conducted for one representative chemical in each group. The variance is typically one to two orders of magnitude. For comparison, the point estimates in potential dose for 236 chemicals span ten orders of magnitude. Most of the variance in the potential dose is due to chemical-specific input parameters, especially half-lives, although exposure factors such as fish intake and the source of drinking water can be important for chemicals whose dominant exposure is through indirect routes. Landscape characteristics are generally of minor importance.