Latent Gaussian models (LGMs) are perhaps the most commonly used class of statistical models with broad applications in various fields, including biostatistics, econometrics, and spatial modeling. LGMs assume that a set of unobserved or latent variables follow a Gaussian distribution, commonly used to model spatial and temporal dependence in the data. The availability of computational tools, such as R-INLA, that permit fast and accurate estimation of LGMs has made their use widespread. Nevertheless, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and predictions made from an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can automatically handle these non-Gaussian features by assuming more flexible and robust non-Gaussian distributions on the latent variables. However, fast implementation and easy-to-use software are lacking, which prevents LnGMs from becoming widely applicable. This dissertation aims to tackle these challenges and provide ready-to-use implementations for the R-INLA package. We view scientific learning as an iterative process involving model criticism followed by model improvement and robustification. Thus, the first step is to provide a framework that allows researchers to criticize and check the adequacy of an LGM without fitting the more expensive LnGM. We employ concepts from Bayesian sensitivity analysis to check the influence of the latent Gaussian assumption on the statistical answers and Bayesian predictive checking to check if the fitted LGM can predict important features in the data. In many applications, this procedure will suffice to justify using an LGM. For cases where this check fails, we provide fast and scalable implementations of LnGMs based on variational Bayes and Laplace approximations. The approximation leads to an LGM that downweights extreme events in the latent variables, reducing their impact and leading to more robust inferences. Each step, the first of LGM criticism and the second of LGM robustification, can be executed in R-INLA, requiring only the addition of a few lines of code. This results in a robust workflow that applied researchers can readily use.

As ML (Machine Learning) and deep neural networks get more used in many systems,the need to understand and test such systems becomes more actual. When designing a newsystem that contains ML models, the safety of this system becomes inevitably important.This rises the need to discuss a strategy to deal with the potential problems and weak-nesses in such a system. This thesis provides findings from literature and illustrates thepotential strategies in the area of image recognition in a comprehensive way. Lastly, theresult presented in this thesis shows that using an ML component in a complex softwaresystem with high safety requirements requires adopting software methodologies, such asMLOps (Machine learning operations) to monitor such a system and give suggestions tohow to test and verify an ML model integrated into a larger software system.

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Highway bridges are among the most vulnerable and expensive components in transportation networks. In response, the Government of Ontario has allocated $26 billion in the next 10 years to address issues pertaining to aging bridge and deteriorating highway infrastructure in the province. Although several approaches have been developed to guide their rehabilitation, most bridge rehabilitation approaches are focused on the component level (individual bridge) in a relative isolation of other bridges in the network. The current study utilizes a complex network theoretic approach to quantify the topological characteristics of the Ontario Bridge Network (OBN) and subsequently evaluate the OBN robustness and vulnerability characteristics. These measures are then integrated in the development of a Multi Scale Bridge Classification (MSBC) approach—an innovative classification approach that links the OBN component level data (i.e., Bridge Condition Index and year of construction, etc.) to the corresponding dynamic network-level measures. The novel approach calls for a paradigm shift in the strategy governing classifying and prioritizing bridge rehabilitation projects based on bridge criticality within the entire network, rather than only the individual bridge’s structural conditions. The model was also used to identify the most critical bridges in the OBN under different disruptions to facilitate rapid implementation of the study results. / Thesis / Master of Applied Science (MASc)

Yes / Assuring safety and thereby certifying is a key challenge of many kinds of Machine Learning (ML) Models. ML is one of the most widely used technological solutions to automate complex tasks such as autonomous driving, traffic sign recognition, lane keep assist etc. The application of ML is making a significant contributions in the automotive industry, it introduces concerns related to the safety and security of these systems. ML models should be robust and reliable throughout and prove their trustworthiness in all use cases associated with vehicle operation. Proving confidence in the safety and security of ML-based systems and there by giving assurance to regulators, the certification authorities, and other stakeholders is an important task. This paper proposes a framework to handle uncertainties of ML model to improve the safety level and thereby certify the ML Models in the automotive industry.

Design optimality plays a central role in the area of statistical experimental design. In general, problems in design optimality are composed of two vital, but separable, components. One of these is determining conditions under which a design is optimal (such as criterion bounds, values of design parameters, or special structure in the information matrix). The other is construction of designs satisfying those conditions. Most papers deal with either optimality conditions, or design construction in accordance with desired combinatorial properties, but not both. This dissertation determines optimal designs for three treatments in the one-way and multi-way heterogeneity settings, first proving optimality through a series of bounding arguments, then applying combinatorial techniques for their construction. Among the results established are optimality with respect to the well known E and A criteria. A- and E-optimal block designs and row-column designs with three treatments are found, for any parameter set. E-optimal hyperrectangles with three treatments are also found, for any parameter set. Systems of distinct representatives theory is used for the construction of optimal designs. Efficiencies relative to optimal criterion values are used to determine robustness of block designs against loss of a small number of blocks. Nonisomorphic bal anced incomplete block designs are ranked based on their robustness. A complete list of most robust BIBDs for v ≤ 10, r ≤ 15 is compiled. / Ph. D.

Le terme de robustesse structurale donne lieu à diverses définitions et domaines d'application. Dans le domaine de l'ingénierie structurale, le cadre réglementaire des Eurocodes définit la robustesse structurale comme « l'aptitude d'une structure à résister à des événements tels que les incendies, les explosions, les chocs ou les conséquences d'une erreur humaine, sans présenter de dégâts disproportionnés par rapport à la cause d'origine ». Cette définition fait clairement ressortir les notions de dommage initial (défaillance locale) et de dommage disproportionné (défaillance globale). Cette thèse propose une approche de la quantification de la robustesse structurale en contexte probabiliste pour mesurer l'impact d'une défaillance localisée sur la défaillance globale de la structure. L'objectif majeur de la thèse est de quantifier l'écart entre une défaillance locale et une défaillance globale, en introduisant différents indices de robustesse selon que la structure soit intègre ou initialement endommagée. Pour cela, dans le but de caractériser et quantifier les liens existant entre la performance des différents éléments d'une structure et la performance globale de la structure, il est nécessaire d'introduire une étude en système qui intègre de manière concomitante des notions de défaillance locale (modes de défaillance) et des notions de défaillance globale. Une recherche « par l'intérieur » des chemins de défaillance dominants est présentée. Le terme « par l'intérieur » est utilisé car c'est le cheminement interne de la défaillance dans la structure qui est recherché. Des méthodes de parcours d'arbre d'évènements sont introduites telles que la méthode des « branches et bornes », du β-unzipping, ou encore du β-unzipping avec bornage. Ces méthodes permettent d'identifier les chemins de défaillance dominants avec des temps de calcul raisonnables. En particulier, il est possible de déterminer le chemin de défaillance associé à la plus grande probabilité de défaillance, appelé encore chemin de référence. Une approche « par l'extérieur » est également proposée, qui consiste à identifier la défaillance globale sans parcourir un arbre d'évènement (et donc sans s'intéresser à l'ordre avec lequel la défaillance survient). Le terme « par l'extérieur » correspond donc à regarder la défaillance de manière globale sans chercher à déterminer la chronologie de la défaillance. Dans les deux cas, l'enjeu est au final de développer une démarche globale permettant d'apprécier et de quantifier la robustesse des structures neuves ou existantes au travers de méthodes et d'indices pouvant s'appliquer à une large variété de problèmes / Structural robustness is associated with several definitions depending on context. In the field of structural engineering, the Eurocodes define structural robustness as “the ability of a structure to withstand events like fire, explosions, impact or the consequences of human error, without being damaged to an extent disproportionate to the original cause”. Such a definition clearly involves concepts of local and global failures. This PhD work proposes a methodology to quantify structural robustness in a probabilistic way and to assess the impact of local failures on global failures. The main objective of this PhD is to quantify the gap between local and global failures by introducing several robustness indices proposed for undamaged and damaged structures. To qualify and quantify the relationships between the performance of the different structural components and the overall structural performance, it is necessary to introduce a system-level analysis which simultaneously considers concepts of local failure modes and global failure events. An inner approach is introduced to determine significant failure sequences and to characterize stochastically dominant failure paths identified by using branch-and-bound, β-unzipping, and mixed β-unzipping with bounding methods. These methods enable to determine significant failure paths with reasonable computational times. In particular, the path with the largest probability of occurrence is considered as the reference failure path. An outer approach is also proposed which identifies global failure without using an event-tree search (and, consequently, without analyzing the order in the failure sequence). This concept characterizes an overall and simultaneous failure of different components without determining the chronology in the failure event. In both cases, the goal is to provide a general and widely applicable framework for qualifying and quantifying the robustness level of new and existing structures through the introduction of methodologies and indices

La mise en oeuvre de systèmes autonomes nécessite le développement et l'utilisation d'architectures logicielles multi-couches qui soient adaptées. Typiquement, une couche fonctionnelle renferme des modules en charge de commander les éléments matériels du système et de fournir des services élémentaires. Pour être robuste, la couche fonctionnelle doit être dotée de mécanismes de protection vis-à-vis de requêtes erronées ou inopportunes issues de la couche supérieure. Nous présentons une méthodologie pour tester la robustesse de ces mécanismes. Nous définissons un cadre général pour évaluer la robustesse d'une couche fonctionnelle par la caractérisation de son comportement vis-à-vis de requêtes inopportunes. Nous proposons également un environnement de validation basé sur l'injection de fautes dans le logiciel de commande d'un robot simulé. Un grand nombre de cas de tests est généré automatiquement par la mutation d'une séquence de requêtes valides. Les statistiques descriptives des comportements en présence de requêtes inopportunes sont analysées afin d'évaluer la robustesse du système sous test. / The implementation of autonomous systems requires the development and the using of multi-layer software architecture. Typically, a functional layer contains several modules that control the material of the system and provide elementary services. To be robust, the functional layer must be implemented with protection mechanisms with respect to erroneous or inopportune requests sent from the superior layer. We present a methodology for robustness testing these mechanisms. We define a general framework to evaluate the robustness of a functional layer by characterizing its behavior with respect to inappropriate requests. We also propose an validation environment based on fault injection in the control software of a simulated robot. A great number of test cases is generated automatically by the mutation of a sequence of valid requests. The descriptive statistics of the behaviors in the presence of inappropriate requests are analyzed in order to evaluate the robustness of the system under test.