Graphical probabilistic analysis of the combination of items of evidence

Unlike the evaluation of single items of scientific evidence, the formal study and analysis of the jointevaluation of several distinct items of forensic evidence has to date received some punctual, ratherthan systematic, attention. Questions about the (i) relationships among a set of (usually unobservable)propositions and a set of (observable) items of scientific evidence, (ii) the joint probative valueof a collection of distinct items of evidence as well as (iii) the contribution of each individual itemwithin a given group of pieces of evidence still represent fundamental areas of research. To somedegree, this is remarkable since both, forensic science theory and practice, yet many daily inferencetasks, require the consideration of multiple items if not masses of evidence. A recurrent and particularcomplication that arises in such settings is that the application of probability theory, i.e. the referencemethod for reasoning under uncertainty, becomes increasingly demanding. The present paper takesthis as a starting point and discusses graphical probability models, i.e. Bayesian networks, as frameworkwithin which the joint evaluation of scientific evidence can be approached in some viable way.Based on a review of existing main contributions in this area, the article here aims at presentinginstances of real case studies from the author's institution in order to point out the usefulness andcapacities of Bayesian networks for the probabilistic assessment of the probative value of multipleand interrelated items of evidence. A main emphasis is placed on underlying general patterns of inference,their representation as well as their graphical probabilistic analysis. Attention is also drawnto inferential interactions, such as redundancy, synergy and directional change. These distinguish thejoint evaluation of evidence from assessments of isolated items of evidence. Together, these topicspresent aspects of interest to both, domain experts and recipients of expert information, because theyhave bearing on how multiple items of evidence are meaningfully and appropriately set into context.

Machine learning for geospatial data : algorithms, software tools and case studies

Résumé Cette thèse est consacrée à l'analyse, la modélisation et la visualisation de données environnementales à référence spatiale à l'aide d'algorithmes d'apprentissage automatique (Machine Learning). L'apprentissage automatique peut être considéré au sens large comme une sous-catégorie de l'intelligence artificielle qui concerne particulièrement le développement de techniques et d'algorithmes permettant à une machine d'apprendre à partir de données. Dans cette thèse, les algorithmes d'apprentissage automatique sont adaptés pour être appliqués à des données environnementales et à la prédiction spatiale. Pourquoi l'apprentissage automatique ? Parce que la majorité des algorithmes d'apprentissage automatiques sont universels, adaptatifs, non-linéaires, robustes et efficaces pour la modélisation. Ils peuvent résoudre des problèmes de classification, de régression et de modélisation de densité de probabilités dans des espaces à haute dimension, composés de variables informatives spatialisées (« géo-features ») en plus des coordonnées géographiques. De plus, ils sont idéaux pour être implémentés en tant qu'outils d'aide à la décision pour des questions environnementales allant de la reconnaissance de pattern à la modélisation et la prédiction en passant par la cartographie automatique. Leur efficacité est comparable au modèles géostatistiques dans l'espace des coordonnées géographiques, mais ils sont indispensables pour des données à hautes dimensions incluant des géo-features. Les algorithmes d'apprentissage automatique les plus importants et les plus populaires sont présentés théoriquement et implémentés sous forme de logiciels pour les sciences environnementales. Les principaux algorithmes décrits sont le Perceptron multicouches (MultiLayer Perceptron, MLP) - l'algorithme le plus connu dans l'intelligence artificielle, le réseau de neurones de régression généralisée (General Regression Neural Networks, GRNN), le réseau de neurones probabiliste (Probabilistic Neural Networks, PNN), les cartes auto-organisées (SelfOrganized Maps, SOM), les modèles à mixture Gaussiennes (Gaussian Mixture Models, GMM), les réseaux à fonctions de base radiales (Radial Basis Functions Networks, RBF) et les réseaux à mixture de densité (Mixture Density Networks, MDN). Cette gamme d'algorithmes permet de couvrir des tâches variées telle que la classification, la régression ou l'estimation de densité de probabilité. L'analyse exploratoire des données (Exploratory Data Analysis, EDA) est le premier pas de toute analyse de données. Dans cette thèse les concepts d'analyse exploratoire de données spatiales (Exploratory Spatial Data Analysis, ESDA) sont traités selon l'approche traditionnelle de la géostatistique avec la variographie expérimentale et selon les principes de l'apprentissage automatique. La variographie expérimentale, qui étudie les relations entre pairs de points, est un outil de base pour l'analyse géostatistique de corrélations spatiales anisotropiques qui permet de détecter la présence de patterns spatiaux descriptible par une statistique. L'approche de l'apprentissage automatique pour l'ESDA est présentée à travers l'application de la méthode des k plus proches voisins qui est très simple et possède d'excellentes qualités d'interprétation et de visualisation. Une part importante de la thèse traite de sujets d'actualité comme la cartographie automatique de données spatiales. Le réseau de neurones de régression généralisée est proposé pour résoudre cette tâche efficacement. Les performances du GRNN sont démontrées par des données de Comparaison d'Interpolation Spatiale (SIC) de 2004 pour lesquelles le GRNN bat significativement toutes les autres méthodes, particulièrement lors de situations d'urgence. La thèse est composée de quatre chapitres : théorie, applications, outils logiciels et des exemples guidés. Une partie importante du travail consiste en une collection de logiciels : Machine Learning Office. Cette collection de logiciels a été développée durant les 15 dernières années et a été utilisée pour l'enseignement de nombreux cours, dont des workshops internationaux en Chine, France, Italie, Irlande et Suisse ainsi que dans des projets de recherche fondamentaux et appliqués. Les cas d'études considérés couvrent un vaste spectre de problèmes géoenvironnementaux réels à basse et haute dimensionnalité, tels que la pollution de l'air, du sol et de l'eau par des produits radioactifs et des métaux lourds, la classification de types de sols et d'unités hydrogéologiques, la cartographie des incertitudes pour l'aide à la décision et l'estimation de risques naturels (glissements de terrain, avalanches). Des outils complémentaires pour l'analyse exploratoire des données et la visualisation ont également été développés en prenant soin de créer une interface conviviale et facile à l'utilisation. Machine Learning for geospatial data: algorithms, software tools and case studies Abstract The thesis is devoted to the analysis, modeling and visualisation of spatial environmental data using machine learning algorithms. In a broad sense machine learning can be considered as a subfield of artificial intelligence. It mainly concerns with the development of techniques and algorithms that allow computers to learn from data. In this thesis machine learning algorithms are adapted to learn from spatial environmental data and to make spatial predictions. Why machine learning? In few words most of machine learning algorithms are universal, adaptive, nonlinear, robust and efficient modeling tools. They can find solutions for the classification, regression, and probability density modeling problems in high-dimensional geo-feature spaces, composed of geographical space and additional relevant spatially referenced features. They are well-suited to be implemented as predictive engines in decision support systems, for the purposes of environmental data mining including pattern recognition, modeling and predictions as well as automatic data mapping. They have competitive efficiency to the geostatistical models in low dimensional geographical spaces but are indispensable in high-dimensional geo-feature spaces. The most important and popular machine learning algorithms and models interesting for geo- and environmental sciences are presented in details: from theoretical description of the concepts to the software implementation. The main algorithms and models considered are the following: multi-layer perceptron (a workhorse of machine learning), general regression neural networks, probabilistic neural networks, self-organising (Kohonen) maps, Gaussian mixture models, radial basis functions networks, mixture density networks. This set of models covers machine learning tasks such as classification, regression, and density estimation. Exploratory data analysis (EDA) is initial and very important part of data analysis. In this thesis the concepts of exploratory spatial data analysis (ESDA) is considered using both traditional geostatistical approach such as_experimental variography and machine learning. Experimental variography is a basic tool for geostatistical analysis of anisotropic spatial correlations which helps to understand the presence of spatial patterns, at least described by two-point statistics. A machine learning approach for ESDA is presented by applying the k-nearest neighbors (k-NN) method which is simple and has very good interpretation and visualization properties. Important part of the thesis deals with a hot topic of nowadays, namely, an automatic mapping of geospatial data. General regression neural networks (GRNN) is proposed as efficient model to solve this task. Performance of the GRNN model is demonstrated on Spatial Interpolation Comparison (SIC) 2004 data where GRNN model significantly outperformed all other approaches, especially in case of emergency conditions. The thesis consists of four chapters and has the following structure: theory, applications, software tools, and how-to-do-it examples. An important part of the work is a collection of software tools - Machine Learning Office. Machine Learning Office tools were developed during last 15 years and was used both for many teaching courses, including international workshops in China, France, Italy, Ireland, Switzerland and for realizing fundamental and applied research projects. Case studies considered cover wide spectrum of the real-life low and high-dimensional geo- and environmental problems, such as air, soil and water pollution by radionuclides and heavy metals, soil types and hydro-geological units classification, decision-oriented mapping with uncertainties, natural hazards (landslides, avalanches) assessments and susceptibility mapping. Complementary tools useful for the exploratory data analysis and visualisation were developed as well. The software is user friendly and easy to use.

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): likelihood ratio calculation and case pre-assessment using Bayesian networks

Well developed experimental procedures currently exist for retrieving and analyzing particle evidence from hands of individuals suspected of being associated with the discharge of a firearm. Although analytical approaches (e.g. automated Scanning Electron Microscopy with Energy Dispersive X-ray (SEM-EDS) microanalysis) allow the determination of the presence of elements typically found in gunshot residue (GSR) particles, such analyses provide no information about a given particle's actual source. Possible origins for which scientists may need to account for are a primary exposure to the discharge of a firearm or a secondary transfer due to a contaminated environment. In order to approach such sources of uncertainty in the context of evidential assessment, this paper studies the construction and practical implementation of graphical probability models (i.e. Bayesian networks). These can assist forensic scientists in making the issue tractable within a probabilistic perspective. The proposed models focus on likelihood ratio calculations at various levels of detail as well as case pre-assessment.

Functions of the peroxisome proliferator-activated receptor (PPAR) alpha and beta in skin homeostasis, epithelial repair, and morphogenesis.

The three peroxisome proliferator-activated receptors (PPAR alpha, PPAR beta, and PPAR gamma) are ligand-activated transcription factors belonging to the nuclear hormone receptor superfamily. They are regarded as being sensors of physiological levels of fatty acids and fatty acid derivatives. In the adult mouse skin, they are found in hair follicle keratinocytes but not in interfollicular epidermis keratinocytes. Skin injury stimulates the expression of PPAR alpha and PPAR beta at the site of the wound. Here, we review the spatiotemporal program that triggers PPAR beta expression immediately after an injury, and then gradually represses it during epithelial repair. The opposing effects of the tumor necrosis factor-alpha and transforming growth factor-beta-1 signalling pathways on the activity of the PPAR beta promoter are the key elements of this regulation. We then compare the involvement of PPAR beta in the skin in response to an injury and during hair morphogenesis, and underscore the similarity of its action on cell survival in both situations.

Calcineurin as a Multifunctional Regulator: Unraveling Novel Functions in Fungal Stress Responses, Hyphal Growth, Drug Resistance, and Pathogenesis.

Calcineurin signaling plays diverse roles in fungi in regulating stress responses, morphogenesis and pathogenesis. Although calcineurin signaling is conserved among fungi, recent studies indicate important divergences in calcineurin-dependent cellular functions among different human fungal pathogens. Fungal pathogens utilize the calcineurin pathway to effectively survive the host environment and cause life-threatening infections. The immunosuppressive calcineurin inhibitors (FK506 and cyclosporine A) are active against fungi, making targeting calcineurin a promising antifungal drug development strategy. Here we summarize current knowledge on calcineurin in yeasts and filamentous fungi, and review the importance of understanding fungal-specific attributes of calcineurin to decipher fungal pathogenesis and develop novel antifungal therapeutic approaches.

Tissue-specific opposing functions of the inflammasome adaptor ASC in the regulation of epithelial skin carcinogenesis.

A chronic inflammatory microenvironment favors tumor progression through molecular mechanisms that are still incompletely defined. In inflammation-induced skin cancers, IL-1 receptor- or caspase-1-deficient mice, or mice specifically deficient for the inflammasome adaptor protein ASC (apoptosis-associated speck-like protein containing a CARD) in myeloid cells, had reduced tumor incidence, pointing to a role for IL-1 signaling and inflammasome activation in tumor development. However, mice fully deficient for ASC were not protected, and mice specifically deficient for ASC in keratinocytes developed more tumors than controls, suggesting that, in contrast to its proinflammatory role in myeloid cells, ASC acts as a tumor-suppressor in keratinocytes. Accordingly, ASC protein expression was lost in human cutaneous squamous cell carcinoma, but not in psoriatic skin lesions. Stimulation of primary mouse keratinocytes or the human keratinocyte cell line HaCaT with UVB induced an ASC-dependent phosphorylation of p53 and expression of p53 target genes. In HaCaT cells, ASC interacted with p53 at the endogenous level upon UVB irradiation. Thus, ASC in different tissues may influence tumor growth in opposite directions: it has a proinflammatory role in infiltrating cells that favors tumor development, but it also limits keratinocyte proliferation in response to noxious stimuli, possibly through p53 activation, which helps suppressing tumors.

Antagonistic functions of LMNA isoforms in energy expenditure and lifespan.

Alternative RNA processing of LMNA pre-mRNA produces three main protein isoforms, that is, lamin A, progerin, and lamin C. De novo mutations that favor the expression of progerin over lamin A lead to Hutchinson-Gilford progeria syndrome (HGPS), providing support for the involvement of LMNA processing in pathological aging. Lamin C expression is mutually exclusive with the splicing of lamin A and progerin isoforms and occurs by alternative polyadenylation. Here, we investigate the function of lamin C in aging and metabolism using mice that express only this isoform. Intriguingly, these mice live longer, have decreased energy metabolism, increased weight gain, and reduced respiration. In contrast, progerin-expressing mice show increased energy metabolism and are lipodystrophic. Increased mitochondrial biogenesis is found in adipose tissue from HGPS-like mice, whereas lamin C-only mice have fewer mitochondria. Consistently, transcriptome analyses of adipose tissues from HGPS and lamin C-only mice reveal inversely correlated expression of key regulators of energy expenditure, including Pgc1a and Sfrp5. Our results demonstrate that LMNA encodes functionally distinct isoforms that have opposing effects on energy metabolism and lifespan in mammals.

Redundant functions of TCF-1 and LEF-1 during T and NK cell development, but unique role of TCF-1 for Ly49 NK cell receptor acquisition.

Members of the TCF/LEF (T cell factor / lymphoid enhancer factor) family of DNA-binding factors play important roles during embryogenesis, the establishment and/or maintenance of self-renewing tissues such as the immune system and for malignant transformation. Specifically, it has been shown that TCF-1 is required for T cell development. A role for LEF-1 became apparent when mice harbored two hypomorphic TCF-1 alleles and consequently expressed low levels of TCF-1. Here we show that NK cell development is similarly regulated by redundant functions of TCF-1 and LEF-1, whereby TCF-1 contributes significantly more to NK cell development than LEF-1. Despite this role for NK cell development, LEF-1 is not required for the establishment of a repertoire of MHC class I-specific Ly49 receptors on NK cells. The proper formation of this repertoire depends to a large extent on TCF-1. These findings suggest common and distinct functions of TCF-1 and LEF-1 during lymphocyte development.

Functions of the human papillomavirus type 16 E4 protein

1. Abstract Cervical cancer is thought to be the consequence of infection by human papillomaviruses (HPV). In the majority of cases, DNA from HPV type 16 (HPV16) is found in malignant cervical lesions. The initial steps leading to transformation of an infected cell are not clearly understood but in most cases, disruption and integration of the episomal viral DNA must take place. As a consequence, the E2 and E4 genes are usually not expressed whereas the E6 and E7 oncogenes are highly expressed. However, in a normal infection in which the viral DNA is maintained as an episome, all viral genes are expressed. The pattern according to which the viral proteins are made, and therefore the life cycle of the virus, is tightly linked to the differentiation process of the host keratinocyte. The study of the viral oncogenes E6 and E7 has revealed crucial functions in the process of malignant transformation such as degradation of the p53 tumor suppressor protein, deregulation of the Retinoblastoma protein pathway and activation of the telomerase ribonucleoprotein. All these steps are necessary for cancerous lesions to develop. However, the loss of the E2 gene product seems to be necessary for sufficient expression of E6 and E7 in order to achieve such effects. In normal infections, the E4 protein is made abundantly in the later stages of the viral life cycle. Though extensive amounts of work have been carried out to define the function of E4, it still remains unclear. In this study, several approaches have been used to try and determine the functions of E4. First, a cell-penetrating fusion protein was designed and produced in order to circumvent the chronic difficulties of expressing E4 in mammalian cells. Unfortunately, this approach was not successful due to precipitation of the purified fusion protein. Second, the observation that E4 accumulates in cells having modified their adhesion properties led to the hypothesis that E4 might be involved in the differentiation process of keratinocytes. Preliminary results suggest that E4 triggers differentiation. Last, as E4 has been reported to collapse the cytokeratin network of keratinocytes, a direct approach using atomic force microscopy has allowed us to test the potential modification of mechanical properties of cells harboring reorganized cytokeratin networks. If so, a potential role for E4 in viral particle release could be hypothesized. 2. Résumé Il a été établi que le cancer du col de l'utérus se développe essentiellement à la suite d'une infection par le virus du papillome humain (HPV). Dans la majorité des cas analysés, de l'ADN du HPV de type 16 (HPV16) est détecté. Les étapes initiales de la transformation d'une cellule infectée sont mal connues mais il semble qu'une rupture du génome viral, normalement épisomal, suivi d'une intégration dans le génome de la cellule hôte soient des étapes nécessaires dans la plupart des cas. Or il semble qu'il y ait une sélection pour les cas où l'expression des oncogènes viraux E6 et E7 soit favorisée alors que l'expression des gènes E2 et E4 est en général impossible. Par contre, dans une infection dite normale où le génome viral n'est pas rompu, il n'y pas développement de cancer et tous les gènes viraux sont exprimés. L'ordre dans lequel les protéines virales sont produites, et donc le cycle de réplication du virus, est intimement lié au processus de différentiation de la cellule hôte. L'étude des protéines oncogènes E6 et E7 a révélé des fonctions clés dans le processus de transformation des cellules infectées telles que la dégradation du suppresseur de tumeur p53, la dérégulation de la voie de signalisation Rb ainsi que l'activation de la télomérase. Toutes ces activités sont nécessaires au développement de lésions cancéreuses. Toutefois, il semble que l'expression du gène E2 doit être empêchée afin que suffisamment des protéines E6 et E7 soient produites. Lorsque le gène E2 est exprimé, et donc lorsque le génome viral n'est pas rompu, les protéines E6 et E7 n'entraînent pas de telles conséquences. Le gène E4, qui se trouve dans la séquence codante de E2, a aussi besoin d'un génome viral intact pour être exprimé. Dans une infection normale, le gène E4 est exprimé abondamment dans les dernières étapes de la réplication du virus. Bien que de nombreuses études aient été menées afin de déterminer la fonction virale à E4, aucun résultat n'apparaît évident. Dans ce travail, plusieurs approches ont été utilisées afin d'adresser cette question. Premièrement, une protéine de fusion TAT-E4 a été produite et purifiée. Cette protéine, pouvant entrer dans les cellules vivantes par diffusion au travers de la membrane plasmique, aurait permis d'éviter ainsi les problèmes chroniques rencontrés lors de l'expression de E4 dans les cellules mammifères. Malheureusement, cette stratégie n'a pas pu être utilisée à cause de la précipitation de la protéine purifiée. Ensuite, l'observation que E4 s'accumule dans les cellules ayant modifié leurs propriétés d'adhésion a suggéré que E4 pourrait être impliqué dans le procédé de différentiation des kératinocytes. Des résultats préliminaires supportent cette possibilité. Enfin, il a été montré que E4 pouvait induire une réorganisation du réseau des cytokératines. Une approche directe utilisant le microscope à force atomique nous a ainsi permis de tester une potentielle modification des propriétés mécaniques de cellules ayant modifié leur réseau de cytokératines en présence de E4. Si tel est le cas, un rôle dans la libération de particules virales peut être proposé pour E4.

Combined transcriptomic and proteomic studies reveal non-canonical signaling functions in the jasmonate pathway

Abstract Lipid derived signals mediate many stress and defense responses in multicellular eukaryotes. Among these are the jasmonates, potently active signaling compounds in plants. Jasmonic acid (JA) and 12-oxo-phytodienoic acid (OPDA) are the two best known members of the large jasmonate family. This thesis further investigates their roles as signals using genomic and proteomic approaches. The study is based on a simple genetic model involving two key genes. The first is ALLENE OXIDE SYNTHASE (AOS), encoding the most important enzyme in generating jasmonates. The second is CORONATINE INSENSITIVE 1 (COI1), a gene involved in all currently documented canonical signaling responses. We asked the simple question: do null mutations in AOS and COI1 have analogous effects on the transcriptome ? We found that they do not. If most COI1-dependent genes were also AOS-dependent, the expression of a zinc-finger protein was AOS-dependent but was unaffected by the coi1-1 mutation. We thus supposed that a jasmonate member, most probably OPDA, can alter gene expression partially independently of COI1. Conversely, the expression of at least three genes, one of these is a protein kinase, was shown to be COI1-dependent but did not require a functional AOS protein. We conclude that a non-jasmonate signal might alter gene expression through COIL Proteomic comparison of coi1-1 and aos plants confirmed these observations and highlighted probable protein degradation processes controlled by jasmonates and COI1 in the wounded leaf. This thesis revealed new functions for COI1 and for AOS-generated oxylipins in the jasmonate signaling pathway. Résumé Les signaux dérivés d'acides gras sont des médiateurs de réponses aux stress et de la défense des eucaryotes multicellulaires. Parmi eux, les jasmonates sont de puissants composés de sig¬nalisation chez les plantes. L'acide jasmonique (JA) et l'acide 12-oxo-phytodienoïc (OPDA) sont les deux membres les mieux caractérisés de la grande famille des jasmonates. Cette thèse étudie plus profondément leurs rôles de signalisation en utilisant des approches génomique et protéomique. Cette étude est basée sur un modèle génétique simple n'impliquant que deux gènes. Le premier est PALLENE OXYDE SYNTHASE (AOS) qui encode l'enzyme la plus importante pour la fabrication des jasmonates. Le deuxième est CORONATINE INSENSITIVE 1 (COI1) qui est impliqué dans la totalité des réponses aux jasmonates connues à ce jour. Nous avons posé la question suivante : est-ce que les mutations nulles dans les gènes AOS et COI1 ont des effets analogues sur le transcriptome ? Nous avons trouvé que ce n'était pas le cas. Si la majorité des gènes dépendants de COI1 sont également dépendants d'AOS, l'expression d'un gène codant pour une protéine formée de doigts de zinc n'est pas affectée par la mutation de COI1 tout en étant dépendante d'AOS. Nous avons donc supposé qu'un membre de la famille des jasmonates, probablement OPDA, pouvait modifier l'expression de certains gènes indépendamment de COI1. Inversement, nous avons montré que, tout en étant dépendante de COI1, l'expression d'au moins trois gènes, dont un codant pour une protéine kinase, n'était pas affectée par l'absence d'une protéine AOS fonctionnelle. Nous en avons conclu qu'un signal autre qu'un jasmonate devait modifier l'expression de certains gènes à travers COI1. La comparaison par protéomique de plantes aos et coi1-1 a confirmé ces observations et a mis en évidence un probable processus de dégradation de protéines contrôlé par les jasmonates et COU_ Cette thèse a mis en avant de nouvelles fonctions pour COI1 et pour des oxylipines générées par AOS dans le cadre de la signalisation par les jasmonates.

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.