Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Analysis, modelling and classification of geospatial data using machine learning

The research considers the problem of spatial data classification using machine learning algorithms: probabilistic neural networks (PNN) and support vector machines (SVM). As a benchmark model simple k-nearest neighbor algorithm is considered. PNN is a neural network reformulation of well known nonparametric principles of probability density modeling using kernel density estimator and Bayesian optimal or maximum a posteriori decision rules. PNN is well suited to problems where not only predictions but also quantification of accuracy and integration of prior information are necessary. An important property of PNN is that they can be easily used in decision support systems dealing with problems of automatic classification. Support vector machine is an implementation of the principles of statistical learning theory for the classification tasks. Recently they were successfully applied for different environmental topics: classification of soil types and hydro-geological units, optimization of monitoring networks, susceptibility mapping of natural hazards. In the present paper both simulated and real data case studies (low and high dimensional) are considered. The main attention is paid to the detection and learning of spatial patterns by the algorithms applied.

Decision-making in pediatrics: a practical algorithm to evaluate complementary and alternative medicine for children.

We herein present a preliminary practical algorithm for evaluating complementary and alternative medicine (CAM) for children which relies on basic bioethical principles and considers the influence of CAM on global child healthcare. CAM is currently involved in almost all sectors of pediatric care and frequently represents a challenge to the pediatrician. The aim of this article is to provide a decision-making tool to assist the physician, especially as it remains difficult to keep up-to-date with the latest developments in the field. The reasonable application of our algorithm together with common sense should enable the pediatrician to decide whether pediatric (P)-CAM represents potential harm to the patient, and allow ethically sound counseling. In conclusion, we propose a pragmatic algorithm designed to evaluate P-CAM, briefly explain the underlying rationale and give a concrete clinical example.

Recent misconceptions about the "database search problem": a probabilistic analysis using Bayesian networks

This paper analyses and discusses arguments that emerge from a recent discussion about the proper assessment of the evidential value of correspondences observed between the characteristics of a crime stain and those of a sample from a suspect when (i) this latter individual is found as a result of a database search and (ii) remaining database members are excluded as potential sources (because of different analytical characteristics). Using a graphical probability approach (i.e., Bayesian networks), the paper here intends to clarify that there is no need to (i) introduce a correction factor equal to the size of the searched database (i.e., to reduce a likelihood ratio), nor to (ii) adopt a propositional level not directly related to the suspect matching the crime stain (i.e., a proposition of the kind 'some person in (outside) the database is the source of the crime stain' rather than 'the suspect (some other person) is the source of the crime stain'). The present research thus confirms existing literature on the topic that has repeatedly demonstrated that the latter two requirements (i) and (ii) should not be a cause of concern.

MBIS: multivariate Bayesian image segmentation tool.

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multichannel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Toxic substances in blood: an analysis of current recommendations under a Bayesian (decision) approach

This article extends existing discussion in literature on probabilistic inference and decision making with respect to continuous hypotheses that are prevalent in forensic toxicology. As a main aim, this research investigates the properties of a widely followed approach for quantifying the level of toxic substances in blood samples, and to compare this procedure with a Bayesian probabilistic approach. As an example, attention is confined to the presence of toxic substances, such as THC, in blood from car drivers. In this context, the interpretation of results from laboratory analyses needs to take into account legal requirements for establishing the 'presence' of target substances in blood. In a first part, the performance of the proposed Bayesian model for the estimation of an unknown parameter (here, the amount of a toxic substance) is illustrated and compared with the currently used method. The model is then used in a second part to approach-in a rational way-the decision component of the problem, that is judicial questions of the kind 'Is the quantity of THC measured in the blood over the legal threshold of 1.5 μg/l?'. This is pointed out through a practical example.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

Efficient total variation algorithm for fetal brain MRI reconstruction.

Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy, Total Variation (TV)- based energies and more recently non-local means. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm or fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n2) and O(1/√ε), while existing techniques are in O(1/n2) and O(1/√ε). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations.

BACKGROUND: The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. RESULTS: Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. CONCLUSION: ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Improvement of therapeutic drug monitoring of imatinib by Bayesian prediction of trough levels. Personalized drug dosage

Aims: Plasma concentrations of imatinib differ largely between patients despite same dosage, owing to large inter-individual variability in pharmacokinetic (PK) parameters. As the drug concentration at the end of the dosage interval (Cmin) correlates with treatment response and tolerability, monitoring of Cmin is suggested for therapeutic drug monitoring (TDM) of imatinib. Due to logistic difficulties, random sampling during the dosage interval is however often performed in clinical practice, thus rendering the respective results not informative regarding Cmin values.Objectives: (I) To extrapolate randomly measured imatinib concentrations to more informative Cmin using classical Bayesian forecasting. (II) To extend the classical Bayesian method to account for correlation between PK parameters. (III) To evaluate the predictive performance of both methods.Methods: 31 paired blood samples (random and trough levels) were obtained from 19 cancer patients under imatinib. Two Bayesian maximum a posteriori (MAP) methods were implemented: (A) a classical method ignoring correlation between PK parameters, and (B) an extended one accounting for correlation. Both methods were applied to estimate individual PK parameters, conditional on random observations and covariate-adjusted priors from a population PK model. The PK parameter estimates were used to calculate trough levels. Relative prediction errors (PE) were analyzed to evaluate accuracy (one-sample t-test) and to compare precision between the methods (F-test to compare variances).Results: Both Bayesian MAP methods allowed non-biased predictions of individual Cmin compared to observations: (A) - 7% mean PE (CI95% - 18 to 4 %, p = 0.15) and (B) - 4% mean PE (CI95% - 18 to 10 %, p = 0.69). Relative standard deviations of actual observations from predictions were 22% (A) and 30% (B), i.e. comparable to the intraindividual variability reported. Precision was not improved by taking into account correlation between PK parameters (p = 0.22).Conclusion: Clinical interpretation of randomly measured imatinib concentrations can be assisted by Bayesian extrapolation to maximum likelihood Cmin. Classical Bayesian estimation can be applied for TDM without the need to include correlation between PK parameters. Both methods could be adapted in the future to evaluate other individual pharmacokinetic measures correlated to clinical outcomes, such as area under the curve(AUC).

Migrated foreign body liver abscess: illustrative case report, systematic review, and proposed diagnostic algorithm.

Pyogenic liver abscess is a severe condition and a therapeutic challenge. Treatment failure may be due to an unrecognized ingested foreign body that migrated from the gastrointestinal tract. There has recently been a marked increase in the number of reported cases of this condition, but initial misdiagnosis as cryptogenic liver abscess still occurs in the majority of cases. We conducted the current study to characterize this entity and provide a diagnostic strategy applicable worldwide. To this end, data were collected from our case and from a systematic review that identified 59 well-described cases. Another systematic review identified series of cryptogenic-and Asian Klebsiella-liver abscess; these data were pooled and compared with the data from the cases of migrated foreign body liver abscess. The review points out the low diagnostic accuracy of history taking, modern imaging, and even surgical exploration. A fistula found through imaging procedures or endoscopy warrants surgical exploration. Findings suggestive of foreign body migration are symptoms of gastrointestinal perforation, computed tomography demonstration of a thickened gastrointestinal wall in continuity with the abscess, and adhesions seen during surgery. Treatment failure, left lobe location, unique location (that is, only 1 abscess location within the liver), and absence of underlying conditions also point to the diagnosis, as shown by comparison with the cryptogenic liver abscess series. This study demonstrates that migrated foreign body liver abscess is a specific entity, increasingly reported. It usually is not cured when unrecognized, and diagnosis is mainly delayed. This study provides what we consider the best available evidence for timely diagnosis with worldwide applicability. Increased awareness is required to treat this underestimated condition effectively, and further studies are needed.