Dans cette thèse, on propose des techniques d'inférence bayésienne dans les modèles où la vraisemblance possède une composante latente. La vraisemblance d'un jeu de données observé est l'intégrale de la vraisemblance dite complète sur l'espace de la variable latente. On s'intéresse aux cas où l'espace de la variable latente est de très grande dimension et comportes des directions de différentes natures (discrètes et continues), ce qui rend cette intégrale incalculable. Le champs d'application privilégié de cette thèse est l'inférence dans les modèles de génétique des populations. Pour mener leurs études, les généticiens des populations se basent sur l'information génétique extraite des populations du présent et représente la variable observée. L'information incluant l'histoire spatiale et temporelle de l'espèce considérée est inaccessible en général et représente la composante latente. Notre première contribution dans cette thèse suppose que la vraisemblance peut être évaluée via une approximation numériquement coûteuse. Le schéma d'échantillonnage préférentiel adaptatif et multiple (AMIS pour Adaptive Multiple Importance Sampling) de Cornuet et al. [2012] nécessite peu d'appels au calcul de la vraisemblance et recycle ces évaluations. Cet algorithme approche la loi a posteriori par un système de particules pondérées. Cette technique est conçue pour pouvoir recycler les simulations obtenues par le processus itératif (la construction séquentielle d'une suite de lois d'importance). Dans les nombreux tests numériques effectués sur des modèles de génétique des populations, l'algorithme AMIS a montré des performances numériques très prometteuses en terme de stabilité. Ces propriétés numériques sont particulièrement adéquates pour notre contexte. Toutefois, la question de la convergence des estimateurs obtenus parcette technique reste largement ouverte. Dans cette thèse, nous montrons des résultats de convergence d'une version légèrement modifiée de cet algorithme. Sur des simulations, nous montrons que ses qualités numériques sont identiques à celles du schéma original. Dans la deuxième contribution de cette thèse, on renonce à l'approximation de la vraisemblance et onsupposera seulement que la simulation suivant le modèle (suivant la vraisemblance) est possible. Notre apport est un algorithme ABC séquentiel (Approximate Bayesian Computation). Sur les modèles de la génétique des populations, cette méthode peut se révéler lente lorsqu'on vise uneapproximation précise de la loi a posteriori. L'algorithme que nous proposons est une amélioration de l'algorithme ABC-SMC de DelMoral et al. [2012] que nous optimisons en nombre d'appels aux simulations suivant la vraisemblance, et que nous munissons d'un mécanisme de choix de niveauxd'acceptations auto-calibré. Nous implémentons notre algorithme pour inférer les paramètres d'un scénario évolutif réel et complexe de génétique des populations. Nous montrons que pour la même qualité d'approximation, notre algorithme nécessite deux fois moins de simulations par rapport à laméthode ABC avec acceptation couramment utilisée. / This thesis consists of two parts which can be read independently.The first part is about the Adaptive Multiple Importance Sampling (AMIS) algorithm presented in Cornuet et al.(2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of the recycling procedure. These numerical properties are particularly adapted to the Bayesian paradigm in population genetics where the modelization involves a large number of parameters. However, the consistency of the AMIS estimator remains largely open. In this work, we provide a novel Adaptive Multiple Importance Sampling scheme corresponding to a slight modification of Cornuet et al. (2012) proposition that preserves the above-mentioned improvements. Finally, using limit theorems on triangular arrays of conditionally independant random variables, we give a consistensy result for the final particle system returned by our new scheme.The second part of this thesis lies in ABC paradigm. Approximate Bayesian Computation has been successfully used in population genetics models to bypass the calculation of the likelihood. These algorithms provide an accurate estimator by comparing the observed dataset to a sample of datasets simulated from the model. Although parallelization is easily achieved, computation times for assuring a suitable approximation quality of the posterior distribution are still long. To alleviate this issue, we propose a sequential algorithm adapted fromDel Moral et al. (2012) which runs twice as fast as traditional ABC algorithms. Itsparameters are calibrated to minimize the number of simulations from the model.

Ce travail propose de nouvelles méthodes d’évaluation d’indicateurs de risque associés à une stratégie d’investissements, en vue d’une optimisation robuste de la maintenance d’un parc de composants. La quantification de ces indicateurs nécessite une modélisation rigoureuse de l’évolution stochastique des durées de vie des composants soumis à maintenance. Pour ce faire, nous proposons d’utiliser des processus markoviens déterministes par morceaux, qui sont généralement utilisés en Fiabilité Dynamique pour modéliser des composants en interaction avec leur environnement. Les indicateurs de comparaison des stratégies de maintenance candidates sont issus de la Valeur Actuelle Nette (VAN). La VAN représente la différence entre les flux financiers associés à une stratégie de référence et ceux associés à une stratégie de maintenance candidate. D’un point de vue probabiliste, la VAN est la différence de deux variables aléatoires dépendantes, ce qui en complique notablement l’étude. Dans cette thèse, les méthodes de Quasi Monte Carlo sont utilisées comme alternatives à la méthode de Monte Carlo pour la quantification de la loi de la VAN. Ces méthodes sont dans un premier temps appliquées sur des exemples illustratifs. Ensuite, elles ont été adaptées pour l’évaluation de stratégie de maintenance de deux systèmes de composants d’une centrale de production d’électricité. Le couplage de ces méthodes à un algorithme génétique a permis d’optimiser une stratégie d’investissements. / This work proposes new assessment methods of risk indicators associated with an investments plan in view of a robust maintenance optimization of a fleet of components. The quantification of these indicators requires a rigorous modelling of the stochastic evolution of the lifetimes of components subject to maintenance. With that aim, we propose to use Piecewise Deterministic Markov Processes which are usually used in Dynamic Reliability for the modelling of components in interaction with their environment. The comparing indicators of candidate maintenance strategies are derived from the Net Present Value (NPV). The NPV stands for the difference between the cumulated discounted cash-flows of both reference and candidate maintenance strategies. From a probabilistic point of view, the NPV is the difference between two dependent random variables, which complicates its study. In this thesis, Quasi Monte Carlo methods are used as alternatives to Monte Carlo method for the quantification of the NPV probabilistic distribution. These methods are firstly applied to illustrative examples. Then, they were adapted to the assessment of maintenance strategy of two systems of components of an electric power station. The coupling of these methods with a genetic algorithm has allowed to optimize an investments plan.

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods. The first paper develops new expansions of the weakcomputational error for Itˆo stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a posteriori form, and arebased on stochastic flows and discrete dual backward problems.Beside this, these expansions lead to efficient and accuratecomputation of error estimates and give the basis for adaptivealgorithms with either deterministic or stochastic time steps.The second paper proves convergence rates of adaptivealgorithms for Itˆo stochastic differential equations. Twoalgorithms based either on stochastic or deterministic timesteps are studied. The analysis of their numerical complexitycombines the error expansions from the first paper and anextension of the convergence results for adaptive algorithmsapproximating deterministic ordinary differential equations.Both adaptive algorithms are proven to stop with an optimalnumber of time steps up to a problem independent factor definedin the algorithm. The third paper extends the techniques to theframework of Itˆo stochastic differential equations ininfinite dimensional spaces, arising in the Heath Jarrow Mortonterm structure model for financial applications in bondmarkets. Error expansions are derived to identify differenterror contributions arising from time and maturitydiscretization, as well as the classical statistical error dueto finite sampling. The last paper studies the approximation of linear ellipticstochastic partial differential equations, describing andanalyzing two numerical methods. The first method generates iidMonte Carlo approximations of the solution by sampling thecoefficients of the equation and using a standard Galerkinfinite elements variational formulation. The second method isbased on a finite dimensional Karhunen- Lo`eve approximation ofthe stochastic coefficients, turning the original stochasticproblem into a high dimensional deterministic parametricelliptic problem. Then, adeterministic Galerkin finite elementmethod, of either h or p version, approximates the stochasticpartial differential equation. The paper concludes by comparingthe numerical complexity of the Monte Carlo method with theparametric finite element method, suggesting intuitiveconditions for an optimal selection of these methods. 2000Mathematics Subject Classification. Primary 65C05, 60H10,60H35, 65C30, 65C20; Secondary 91B28, 91B70. / QC 20100825

財政部所推動保單紅利自由化及費率自由化政策提供壽險商品市場的另一發展方向，促進我保險市場良性競爭，且自民國九十二年自由分紅保單進入台灣壽險市場，已有數十家壽險公司相繼搶這塊大餅，目前市面上的分紅保單大多採用美式三元利差分紅方式，在紅利部分尚不可設定保證給付，亦即沒有保證保戶每年都一定會領到利差分紅。因此，本研究將介紹在歐洲廣為盛行、附最低保證給付的英式分紅保單，作為國內業者在分紅保單設計上的參考指標。 本研究主要以傳統壽險商品為研究範疇，在不考慮有解約權下以隨機模擬的方式對英式分紅保單進行公平定價。研究方法為在大量模擬下找出不同投資策略的Markowiz效率前緣曲線，並選用這些投資策略於給定不分紅保單的預定利率下，在公平精算原則為前提下以蒙地卡羅法(Monte Carlo Methods)的方式，針對不同目標期末紅利率(Terminal Bonus Target；TB)，找出分紅保單應有的合理預定利率及期間紅利率。再去衡量保險公司不同資產配置下，因為未達到期望紅利所造成的風險。此外，本研究更進一步地以靜態及動態投資策略探討保險公司失去清償能力(Insolvency Risk)的問題。 最後在上述架構下，本研究為了符合市場實際情況，分別針對不同保單期間與不同的繳費方式進行敏感度分析。

The aim of this Thesis is the development of stopping rule methods for the MLEM and OSEM algorithms used in image reconstruction positron emission tomography (PET). The development of the stopping rules is based on the study of the properties of both algorithms. Analyzing their mathematical expressions, it can be observed that the pixel updating coefficients (PUC) play a key role in the upgrading process of the reconstructed image from iteration k to k+1. For the analysis of the properties of the PUC, a PET scanner geometry was simulated using Monte Carlo methods. For image reconstruction using iterative techniques, the calculation of the transition matrix is essential. And it fully depends on the geometrical characteristics of the PET scanner. The MLEM and OSEM algorithms were used to reconstruct the projection data. In order to compare the reconstructed and true images, two figures of merit (FOM) were used; a) the Normalized Root Mean Square Deviation (NRMSD) and b) the chi-square χ2. The behaviour of the PUC C values for a zero and non-zero pixel in the phantom image was analyzed and it has been found different behavior for zero and non-zero pixels. Based on this assumption, the vector of all C values was analyzed for all non-zero pixels of the reconstructed image and it was found that the histograms of the values of the PUC have two components: one component around C(i)=1.0 and a tail component, for values C(i)<1.0. In this way, a vector variable has been defined, where I is the total number of pixels in the image and k is the iteration number. is the minimum value of the vector of the pixel updating coefficients among the non-zero pixels of the reconstructed image at iteration k. Further work was performed to find out the dependence of Cmin on the image characteristics, image topology and activity level. The analysis shows that the parameterization of Cmin is reliable and allows the establishment of a robust stopping rule for the MLEM algorithm. Furthermore, following a different approach, a new stopping rule using the log-likelihood properties of the MLEM algorithm has been developed. The two rules were evaluated using the independent Digimouse phantom. The study revealed that both stopping rules produce reconstructed images with similar properties. The same study was performed for the OSEM algorithm and a stopping rule for the OSEM algorithm dedicated to each number of subset was developed. / Σκοπός της διατριβής είναι η ανάπτυξη κριτηρίων παύσης για τους επαναληπτικούς αλγόριθμους (MLEM και OSEM) που χρησιμοποιούνται στην ανακατασκευή ιατρικής εικόνας στους τομογράφους εκπομπής ποζιτρονίου (PET). Η ανάπτυξη των κριτηρίων παύσης βασίστηκε στη μελέτη των ιδιοτήτων των αλγόριθμων MLEM & OSEM. Απο τη μαθηματική έκφραση των δύο αλγορίθμων προκύπτει ότι οι συντελεστές αναβάθμισης (ΣΑ) των pixels της εικόνας παίζουν σημαντικό ρόλο στην ανακατασκευή της απο επανάληψη σε επανάληψη. Για την ανάλυση ένας τομογράφος PET προσομοιώθηκε με τη χρήση των μεθόδων Μόντε Κάρλο.Για την ανακατασκευή της εικόνας με τη χρήση των αλγόριθμων MLEM και OSEM, υπολογίστηκε ο πίνακας μετάβασης. Ο πίνακας μετάβασης εξαρτάται απο τα γεωμετρικά χαρακτηριστικά του τομογράφου PET και για τον υπολογισμό του χρησιμοποιήθηκαν επίσης μέθοδοι Μόντε Κάρλο. Ως ψηφιακά ομοιώματα χρησιμοποιήθηκαν το ομοίωμα εγκεφάλου Hoffman και το 4D MOBY. Για κάθε ένα απο τα ομοιώματα δημιουργήθηκαν προβολικά δεδομένα σε διαφορετικές ενεργότητες. Για τη σύγκριση της ανακατασκευασμένης και της αρχικής εικόνας χρησιμοποιήθηκαν δύο ξεχωριστοί δείκτες ποίοτητας, το NRMSD και το chi square. Η ανάλυση έδειξε οτι οι ΣΑ για τα μη μηδενικά pixels της εικόνας τείνουν να λάβουν την τιμή 1.0 με την αύξηση των επαναλήψεων, ενώ για τα μηδενικά pixels αυτό δε συμβαίνει. Αναλύοντας περισσότερο το διάνυσμα των ΣΑ για τα μη μηδενικά pixels της ανακατασκευασμένης εικόνας διαπιστώθηκε ότι αυτό έχει δύο μέρη: α) Μια κορυφή για τιμές των ΣΑ = 1.0 και β) μια ουρά με τιμές των ΣΑ<1.0. Αυξάνοντας τις επαναλήψεις, ο αριθμός των pixels με ΣΑ=1.0 αυξάνονταν ενώ ταυτόχρονα η ελάχιστη τιμή του διανύσματος των ΣΑ μετακινούνταν προς το 1.0. Με αυτό τον τρόπο προσδιορίστηκε μια μεταβλητή της μορφής όπου N είναι ο αριθμός των pixels της εικόνας, k η επανάληψη και η ελάχιστη τιμή του διανύσματος των ΣΑ. Η ανάλυση που έγινε έδειξε ότι η μεταβλητή Cmin συσχετίζεται μόνο με την ενεργότητα της εικόνας και όχι με το είδος ή το μέγεθός της. Η παραμετροποίηση αυτής της σχέσης οδήγησε στην ανάπτυξη του κριτηρίου παύσης για τον MLEM αλγόριθμο. Μια άλλη προσέγγιση βασισμένη στις ιδιότητες πιθανοφάνειας του MLEM αλγόριθμου, οδήγησε στην ανάπτυξη ενός διαφορετικού κριτηρίου παύσης του MLEM. Τα δύο κριτήρια αποτιμήθηκαν με τη χρήση του ομοιώματος Digimouse και βρέθηκε να παράγουν παρόμοιες εικόνες. Η ίδια μελέτη έγινε και για τον OSEM αλγόριθμο και αναπτύχθηκε κριτήριο παύσης για διαφορετικό αριθμό subsets.

Submitted by JOÉL VILLAVICENCIO GASTELÚ null (tear_295@hotmail.com) on 2016-03-30T17:36:01Z No. of bitstreams: 1 Dissertação_Rev1_13 - Joel Gastelu.pdf: 3335802 bytes, checksum: 93fbe0689da0072cc77a9120a8e24b02 (MD5) / Rejected by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: O arquivo submetido está sem a ficha catalográfica. A versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorrer qualquer alteração em seu conteúdo após a aprovação. Corrija estas informações e realize uma nova submissão contendo o arquivo correto. Agradecemos a compreensão. on 2016-04-01T13:14:50Z (GMT) / Submitted by JOÉL VILLAVICENCIO GASTELÚ null (tear_295@hotmail.com) on 2016-04-01T19:04:22Z No. of bitstreams: 1 Dissertação_Joel.pdf: 4253690 bytes, checksum: 75d9921d8416eec7341f8bf0e2182766 (MD5) / Rejected by Ana Paula Grisoto (grisotoana@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: A data informada na capa do documento está diferente da data de defesa que consta na ficha catalográfica e folha de aprovação. Corrija esta informação no arquivo PDF e realize uma nova submissão contendo o arquivo correto. Agradecemos a compreensão. on 2016-04-05T13:53:33Z (GMT) / Submitted by JOÉL VILLAVICENCIO GASTELÚ null (tear_295@hotmail.com) on 2016-04-06T22:35:57Z No. of bitstreams: 1 Dissertação_Joel.pdf: 4231140 bytes, checksum: 4bd6143a52dc3a6846abd4f996ba9306 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-04-07T12:21:23Z (GMT) No. of bitstreams: 1 gastelu_jv_me_ilha.pdf: 4231140 bytes, checksum: 4bd6143a52dc3a6846abd4f996ba9306 (MD5) / Made available in DSpace on 2016-04-07T12:21:23Z (GMT). No. of bitstreams: 1 gastelu_jv_me_ilha.pdf: 4231140 bytes, checksum: 4bd6143a52dc3a6846abd4f996ba9306 (MD5) Previous issue date: 2016-03-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho tem-se como objetivo estimar o potencial fotovoltaico devido à instalação de sistemas fotovoltaicos em telhados de áreas residenciais. Na estimação desse potencial foram consideradas quatro grandezas: o nível de irradiação solar, a área aproveitável de telhado para a instalação dos sistemas fotovoltaicos, a eficiência de conversão dos sistemas fotovoltaicos e as probabilidades de instalação dos sistemas fotovoltaicos, que caracterizam as preferências dos habitantes à instalação desses sistemas. Um modelo hierárquico bayesiano foi proposto para o cálculo das probabilidades de instalação dos sistemas fotovoltaicos. Nesse modelo bayesiano é estabelecida uma relação entre as probabilidades de instalação, as variáveis socioeconômicas e as interações entre as subáreas, através de um modelo linear generalizado misto. O cálculo do valor esperado das probabilidades de instalação foi realizado usando o método de Monte Carlo via cadeias de Markov. Os resultados do potencial fotovoltaico são apresentados através de mapas temáticos, que permitem a visualização da distribuição espacial do seu valor esperado. Esta informação pode ajudar as concessionárias de distribuição no planejamento e expansão de suas redes elétricas em regiões com maior potencial de geração fotovoltaica. / The present work aims to estimate the photovoltaic potential for installing solar panel on the rooftop of residential areas. The estimation of this potential considers four quantities: the solar radiation level, rooftop availability for installation of photovoltaic systems, conversion efficiency of the photovoltaic systems and the probabilities for the installation of photovoltaic systems that characterize the preferences of the inhabitants to the installation of such systems. A bayesian hierarchical model is proposed to calculate the installation probabilities of photovoltaic systems. This bayesian model establishes a relation among the installation probabilities, socioeconomic variables and interactions between subareas, through a generalized linear mixed model. The calculation of expected value of installation probabilities in each subarea is performed using the Markov Chain Monte Carlo method. Photovoltaic potential results are presented through thematic maps that allow the visualization of the spatial distribution of its expected value. This information can help to distribution utilities for planning and expansion of their networks in regions with the greatest potential for photovoltaic generation.

Dans les systèmes de perception multicapteurs, un point central concerne le suivi d'objets multiples. Dans mes travaux de thèse, le capteur principal est un télémètre laser à balayage qui perçoit des cibles étendues. Le problème desuivi multi-objets se décompose généralement en plusieurs étapes (détection, association et suivi) réalisées de manière séquentielle ou conjointe. Mes travaux ont permis de proposer des alternatives à ces méthodes en adoptant une approche "track-before-detect" sur cibles distribuées qui permet d'éviter la succession des traitements en proposant un cadre global de résolution de ce problème d'estimation. Dans une première partie, nous proposons une méthode de détection travaillant directement en coordonnées naturelles (polaires) qui exploite les propriétés d'invariance géométrique des objets suivis. Cette solution est ensuite intégrée dans le cadre des approches JPDA et PHD de suivi multicibles résolues grâce aux méthodes de Monte-Carlo séquentielles. La seconde partie du manuscrit vise à s'affranchir du détecteur pour proposer une méthode dans laquelle le modèle d'objet est directement intégré au processus de suivi. C'est sur ce point clé que les avancées ont été les plus significatives permettant d'aboutir à une méthode conjointe de détection et de suivi. Un processus d'agrégation a été développé afin de permettre une formalisation des données qui évite tout prétraitement sous-optimal. Nous avons finalement proposé un formalisme général pour les systèmes multicapteurs (multilidar, centrale inertielle, GPS). D'un point de vue applicatif, ces travaux ont été validés dans le domaine du suivi de véhicules pour les systèmes d'aide à la conduite. / In multi-sensor perception systems, an active topic concerns the multiple object tracking methodes. In this work, the main sensor is a scanning laser rangefinder perceiving extended targets. Tracking methods are generally composed of a three-step scheme (detection, association and tracking) which is jointly or sequentially implemented. This work proposes alternative solutions by considering a track-before-detect approach on extended targets. It avoids the classic procedures by proposing a global framework to solve this estimation problem. Firstly, we propose a detection method dealing with measurements in natural coordinates (polar) which is founded on geometrical invariance properties of the tracked objects. This solution is then integrated in the JPDA and PHD multi-target tracking frameworks solved with the sequential Monte-Carlo methods. The second part of this thesis aims at avoiding the detection step to propose an approach where the object model is directly embedded in the tracking process. This lets to build a novel joint detection and tracking approach. An aggregation process was developed to construct a measurement modeling avoiding any suboptimal preprocessing. We finally proposed a general framework for multi-sensor systems ( multiple lidar, inertial sensor, GPS). Theses methods were applied in the area of multiple vehicle tracking for the Advanced Driver Assistance Systems.

Master of Science / Department of Electrical and Computer Engineering / Faryad Darabi Sahneh / Recent experience of Ebola outbreak of 2014 highlighted the importance of immediate response to impede Ebola transmission at its very early stage. To this aim, efficient and effective allocation of limited resources is crucial. Among standard interventions is the practice of following up with physical contacts of individuals diagnosed with Ebola virus disease -- known as contact tracing. In an effort to objectively understand the effect of possible contact tracing protocols, we explicitly develop a model of Ebola transmission incorporating contact tracing. Our modeling framework has several features to suit early–stage Ebola transmission: 1) the network model is patient–centric because when number of infected cases are small only the myopic networks of infected individuals matter and the rest of possible social contacts are irrelevant, 2) the Ebola disease model is individual–based and stochastic because at the early stages of spread, random fluctuations are significant and must be captured appropriately, 3) the contact tracing model is parameterizable to analyze the impact of critical aspects of contact tracing protocols. Notably, we propose an activity driven network approach to contact tracing, and develop a Monte-Carlo method to compute the basic reproductive number of the disease spread in different scenarios. Exhaustive simulation experiments suggest that while contact tracing is important in stopping the Ebola spread, it does not need to be done too urgently. This result is due to rather long incubation period of Ebola disease infection. However, immediate hospitalization of infected cases is crucial and requires the most attention and resource allocation. Moreover, to investigate the impact of mitigation strategies in the 2014 Ebola outbreak, we consider reported data in Guinea, one the three West Africa countries that had experienced the Ebola virus disease outbreak. We formulate a multivariate sequential Monte Carlo filter that utilizes mechanistic models for Ebola virus propagation to simultaneously estimate the disease progression states and the model parameters according to reported incidence data streams. This method has the advantage of performing the inference online as the new data becomes available and estimating the evolution of the basic reproductive ratio R₀(t) throughout the Ebola outbreak. Our analysis identifies a peak in the basic reproductive ratio close to the time of Ebola cases reports in Europe and the USA.

Orientador: Antônio Padilha Feltrin / Resumo: No presente trabalho tem-se como objetivo estimar o potencial fotovoltaico devido à instalação de sistemas fotovoltaicos em telhados de áreas residenciais. Na estimação desse potencial foram consideradas quatro grandezas: o nível de irradiação solar, a área aproveitável de telhado para a instalação dos sistemas fotovoltaicos, a eficiência de conversão dos sistemas fotovoltaicos e as probabilidades de instalação dos sistemas fotovoltaicos, que caracterizam as preferências dos habitantes à instalação desses sistemas. Um modelo hierárquico bayesiano foi proposto para o cálculo das probabilidades de instalação dos sistemas fotovoltaicos. Nesse modelo bayesiano é estabelecida uma relação entre as probabilidades de instalação, as variáveis socioeconômicas e as interações entre as subáreas, através de um modelo linear generalizado misto. O cálculo do valor esperado das probabilidades de instalação foi realizado usando o método de Monte Carlo via cadeias de Markov. Os resultados do potencial fotovoltaico são apresentados através de mapas temáticos, que permitem a visualização da distribuição espacial do seu valor esperado. Esta informação pode ajudar as concessionárias de distribuição no planejamento e expansão de suas redes elétricas em regiões com maior potencial de geração fotovoltaica. / Abstract: The present work aims to estimate the photovoltaic potential for installing solar panel on the rooftop of residential areas. The estimation of this potential considers four quantities: the solar radiation level, rooftop availability for installation of photovoltaic systems, conversion efficiency of the photovoltaic systems and the probabilities for the installation of photovoltaic systems that characterize the preferences of the inhabitants to the installation of such systems. A bayesian hierarchical model is proposed to calculate the installation probabilities of photovoltaic systems. This bayesian model establishes a relation among the installation probabilities, socioeconomic variables and interactions between subareas, through a generalized linear mixed model. The calculation of expected value of installation probabilities in each subarea is performed using the Markov Chain Monte Carlo method. Photovoltaic potential results are presented through thematic maps that allow the visualization of the spatial distribution of its expected value. This information can help to distribution utilities for planning and expansion of their networks in regions with the greatest potential for photovoltaic generation. / Mestre