Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

Serum polybrominated diphenyl ethers (PBDE) in pooled serum are higher in children (2-5 years of age) than in infants and adults

Background: Polybrominated diphenyl ethers (PBDEs) are used as flame retardants in many products and have been detected in human samples worldwide. Limited data show that concentrations are elevated in young children. Objectives: We investigated the association between PBDEs and age with an emphasis on young children from Australia in 2006–2007. Methods: We collected human blood serum samples (n = 2,420), which we stratified by age and sex and pooled for analysis of PBDEs. Results: The sum of BDE-47, -99, -100, and -153 concentrations (Σ4PBDE) increased from 0–0.5 years (mean ± SD, 14 ± 3.4 ng/g lipid) to peak at 2.6–3 years (51 ± 36 ng/g lipid; p < 0.001) and then decreased until 31–45 years (9.9 ± 1.6 ng/g lipid). We observed no further significant decrease among ages 31–45, 45–60 (p = 0.964), or > 60 years (p = 0.894). The mean Σ4PBDE concentration in cord blood (24 ± 14 ng/g lipid) did not differ significantly from that in adult serum at ages 15–30 (p = 0.198) or 31–45 years (p = 0.140). We found no temporal trend when we compared the present results with Australian PBDE data from 2002–2005. PBDE concentrations were higher in males than in females; however, this difference reached statistical significance only for BDE-153 (p = 0.05). Conclusions: The observed peak concentration at 2.6–3 years of age is later than the period when breast-feeding is typically ceased. This suggests that in addition to the exposure via human milk, young children have higher exposure to these chemicals and/or a lower capacity to eliminate them. Key words: Australia, children, cord blood, human blood serum, PBDEs, polybrominated diphenyl ethers. Environ Health Perspect 117:1461–1465 (2009). doi:10.1289/ehp.0900596

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Context-Based Modelling of Interferometric Signals for the Assessment of Tear-Film Suface Quality

Modelling of interferometric signals related to tear film surface quality is considered. In the context of tear film surface quality estimation in normal healthy eyes, two clinical parameters are of interest: the build-up time, and the average interblink surface quality. The former is closely related to the signal derivative while the latter to the signal itself. Polynomial signal models, chosen for a particular set of noisy interferometric measurements, can be optimally selected, in some sense, with a range of information criteria such as AIC, MDL, Cp, and CME. Those criteria, however, do not always guarantee that the true derivative of the signal is accurately represented and they often overestimate it. Here, a practical method for judicious selection of model order in a polynomial fitting to a signal is proposed so that the derivative of the signal is adequately represented. The paper highlights the importance of context-based signal modelling in model order selection.

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.