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.

Exploration of Daphnia behavioral effect profiles induced by a broad range of toxicants with different modes of action.

Behavior is increasingly reported as a sensitive and early indicator of toxicant stress in aquatic organisms. However, the systematic understanding of behavioral effects and comparisons between effect profiles is hampered because the available studies are limited to few chemicals and differ in the exposure conditions and effect parameters examined. The aims of the present study were 1) to explore behavioral responses of Daphnia magna exposed to different toxicants, 2) to compare behavioral effect profiles with regard to chemical modes of action, and 3) to determine the sensitivity and response time of behavioral parameters in a new multi-cell exposure system named Multi-DaphTrack compared with currently utilized tests. Twelve compounds covering different modes of toxic action were selected to sample a wide range of potential effect profiles. Acute standard immobilization tests and 48 h of behavioral tracking were performed in the customized Multi-DaphTrack system and a single-cell commercialized biological early warning system. Contrasting behavioral profiles were observed for average speed (i.e., intensity, time of effect onset, effect duration), but no distinct behavioral profiles could be drawn from the chemical mode of action. Most compounds tested in the Multi-DaphTrack system induced an early and significant average speed increase at concentrations near or below the 10% effective concentration (48 h) of the acute immobilization test, demonstrating that the Multi-DaphTrack system is fast and sensitive. To conclude, behavior endpoints could be used as an alternative or complement to the current acute standard test or chemical analysis for the predictive evaluation of ecotoxic effects of effluents or water bodies.

Estimating hazardous concentrations by an informative Bayesian approach.

The species sensitivity distribution (SSD) approach is recommended for assessing chemical risk. In practice, however, it can be used only for the few substances for which large-scale ecotoxicological results are available. Indeed, the statistical frequentist approaches used for building SSDs and for deriving hazardous concentrations (HC5) inherently require extensive data to guarantee goodness-of-fit. An alternative Bayesian approach to estimating HC5 from small data sets was developed. In contrast to the noninformative Bayesian approaches that have been tested to date, the authors' method used informative priors related to the expected species sensitivity variance. This method was tested on actual ecotoxicological data for 21 well-informed substances. A cross-validation compared the HC5 values calculated using frequentist approaches with the results of our Bayesian approach, using both complete and truncated data samples. The authors' informative Bayesian approach was compared with noninformative Bayesian methods published in the past, including those incorporating loss functions. The authors found that even for the truncated sample the HC5 values derived from the informative Bayesian approach were generally close to those obtained using the frequentist approach, which requires more data. In addition, the probability of overestimating an HC5 is rather limited. More robust HC5 estimates can be practically obtained from additional data without impairing regulatory protection levels, which will encourage collecting new ecotoxicological data. In conclusion, the Bayesian informative approach was shown to be relatively robust and could be a good surrogate approach for deriving HC5 values from small data sets.

Anatomically informed bayesian model selection for fMRI group data analysis.

A new approach for fMRI group data analysis is introduced to overcome the limitations of standard voxel-based testing methods, such as Statistical Parametric Mapping (SPM). Using a Bayesian model selection framework, the functional network associated with a certain cognitive task is selected according to the posterior probabilities of mean region activations, given a pre-defined anatomical parcellation of the brain. This approach enables us to control a Bayesian risk that balances false positives and false negatives, unlike the SPM-like approach, which only controls false positives. On data from a mental calculation experiment, it detected the functional network known to be involved in number processing, whereas the SPM-like approach either swelled or missed the different activation regions.

Mixed-effect statistics for group analysis in fMRI: a nonparametric maximum likelihood approach.

This technical note describes a collection of test statistics accounting for estimation uncertainties at the within-subject level, that can be used as alternatives to the standard t statistic in one-sample random-effect analyses, i.e. when testing the mean effect of a population. We build such test statistics by estimating the across-subject distribution of the effects using maximum likelihood under a nonparametric mixed-effect model. For inference purposes, the statistics are calibrated using permutation tests to achieve exact false positive control under a symmetry assumption regarding the across-subject distribution. The new tests are implemented in a freely available toolbox for SPM called Distance.

High level group analysis of FMRI data based on Dirichlet process mixture models.

Inferring the position of functionally active regions from a multi-subject fMRI dataset involves the comparison of the individual data and the inference of a common activity model. While voxel-based analyzes, e.g. Random Effect statistics, are widely used, they do not model each individual activation pattern. Here, we develop a new procedure that extracts structures individually and compares them at the group level. For inference about spatial locations of interest, a Dirichlet Process Mixture Model is used. Finally, inter-subject correspondences are computed with Bayesian Network models. We show the power of the technique on both simulated and real datasets and compare it with standard inference techniques.