Exposure of children to extremely low frequency magnetic fields in France: Results of the EXPERS study.

The assessment of magnetic field exposure in children is an important point in the context of epidemiological issues. EXPERS is the first study ever carried out measuring personal exposure to extremely low frequency magnetic fields at a national scale, involving 977 French children with 24 h personal measurements. Descriptive statistical analyses were performed for all the children, and only for children where no alarm clock was identified, as in some cases this requirement of the measurement protocol was not respected. The proportion of children with a 24 h arithmetic mean of ≥0.4 µT was 3.1% when considering all children and 0.8% when excluding alarm clocks. The alarm clocks were the main variable linked to the child exposure measurements. Magnetic field exposure increased when the home was located close to a high voltage power line. However, none of the 0.8% of children living at <125 m to a 225 kV line or <200 m to a 400 kV overhead line had a personal exposure of >0.4 µT. A multiple correspondence analysis showed the difficulty to build a statistical model predicting child exposure. The distribution of child personal exposure was significantly different from the distribution of exposure during sleep, questioning the exposure assessment in some epidemiological studies.

Nonparametric Estimation of the Probability of Detection of Flaws in an Industrial Component, from Destructive and Nondestructive Testing Data, Using Approximate Bayesian Computation.

We consider the problem of estimating the probability of detection (POD) of flaws in an industrial steel component. Modeled as an increasing function of the flaw height, the POD characterizes the detection process; it is also involved in the estimation of the flaw size distribution, a key input parameter of physical models describing the behavior of the steel component when submitted to extreme thermodynamic loads. Such models are used to assess the resistance of highly reliable systems whose failures are seldom observed in practice. We develop a Bayesian method to estimate the flaw size distribution and the POD function, using flaw height measures from periodic in-service inspections conducted with an ultrasonic detection device, together with measures from destructive lab experiments. Our approach, based on approximate Bayesian computation (ABC) techniques, is applied to a real data set and compared to maximum likelihood estimation (MLE) and a more classical approach based on Markov Chain Monte Carlo (MCMC) techniques. In particular, we show that the parametric model describing the POD as the cumulative distribution function (cdf) of a log-normal distribution, though often used in this context, can be invalidated by the data at hand. We propose an alternative nonparametric model, which assumes no predefined shape, and extend the ABC framework to this setting. Experimental results demonstrate the ability of this method to provide a flexible estimation of the POD function and describe its uncertainty accurately.