Au cours des dernières années, les communications inter-véhicule (IVC) sont devenues un domaine de recherche intensif, en particulier dans le cadre des systèmes de transport intelligents. Il suppose que la totalité ou une partie des véhicules est équipé de dispositifs radio permettant la communication entre eux. La norme IEEE 802.11p (normalisé pour la communication des véhicules) devrait être la technologie de facto pour ces communications. En utilisant son mode ad hoc, cette technologie radio permet aux véhicules d'étendre la portée de leur communication en formant un réseau multi-saut sans fil Ad - hoc, également appelé Vehicle ad hoc NETwork (VANET). Cette thèse aborde un problème fondamental des VANET : la capacité du réseau. Deux modèles théoriques simples ont été proposés dans cette thèse pour calculer cette capacité: un « packing problem » (la traduction française nous est inconnue) et un modèle Markovien. Ils offrent des formules simples et fermées sur le nombre maximum d'émetteurs simultanés, et sur la distribution de la distance entre eux. Une borne supérieure sur cette capacité a été proposée. De plus, le modèle Markovien a permis de proposer une formule analytique sur la distribution spatiale des émetteurs. Ces quantités nous permettent, entre autres, de paramétrer le mécanisme d’accès au medium du 802.11p, comme par exemple le seuil du CCA (Clear Channel Assessment), amenant à une optimisation de la capacité du réseau. Afin de valider les différentes contributions théoriques de cette thèse, les résultats des modèles analytiques ont été comparés à des simulations effectuées avec le simulateur de réseau NS-3. Les paramètres de simulations ont été estimés à partir d’expérimentations réelles. De plus, différentes distributions de trafic (trafic de véhicules) ont été considéré afin d’évaluer leur impact sur la capacité du réseau. L’une des applications de cette thèse est le dimensionnement des applications de sécurité routière vis-à-vis de la consommation des ressources réseau. Dans ce cadre, nous nous sommes intéressés aux reconstructions de cartes. Il faut comprendre ICI LA reconstitution de l’environnement d’un véhicule (perception map). Ces applications utilisent des informations provenant de capteurs locaux et distants afin d’offrir un système d’aide à la conduite (conduite autonome, alerte sur des collisions, annonce de situations accidentogènes, etc.). Ces applications nécessitent une bande passante élevée. Notre étude théorique a montré que cette bande passante ne sera sans doute pas disponible en pratique dans les réseaux IEEE 802.11p. Par conséquent, UN algorithme adaptatif de contrôle de puissance a été proposé et optimisé pour cette application particulière. Nous avons montré que notre algorithme, par le biais d'un modèle analytique et d'un grand nombre de simulations que la capacité du réseau est augmentée de manière significative. / In recent years, Inter Vehicle Communication (IVC) has become an intensive research area, as part of Intelligent Transportation Systems. It supposes that all, or a subset of the vehicles is equipped with radio devices, enabling communication between them. IEEE 802.11p (standardized for vehicular communication) shows a great deal of promise. By using ad hoc mode, this radio technology allows vehicles to extend their scopes of communication and thus forming a Multi-hop wireless Ad-hoc NETwork, also called Vehicular Ad-hoc NETwork (VANET). This thesis addresses a fundamental problem of VANET: the network capacity. Two simple theoretical models to estimate this capacity have been proposed: a packing model and a Markovian point process model. They offer simple and closed formulae on the maximum number of simultaneous transmitters, and on the distribution of the distance between them. An accurate upper bound on the maximum capacity had been derived. An analytical formula on distribution of the transmitters had been presented. This distribution allows us to optimize Clear Channel Assessment (CCA) parameters that leads to an optimization of the network capacity.In order to validate the approach of this thesis, results from the analytical models are compared to simulations performed with the network simulator NS-3. Simulation parameters was estimated from real experimentation. Impact of different traffic distributions (traffic of vehicles) on the network capacity is also studied. This thesis also focuses on extended perception map applications, which use information from local and distant sensors to offer driving assistance (autonomous driving, collision warning, etc.). Extended perception requires a high bandwidth that might not be available in practice in classical IEEE 802.11p ad hoc networks. Therefore, this thesis proposes an adaptive power control algorithm optimized for this particular application. It shows through an analytical model and a large set of simulations that the network capacity is then significantly increased.

Change-point detection in hazard rate function is an important research topic in survival analysis. In this dissertation, we firstly review existing methods for single change-point detection in piecewise exponential hazard model. Then we consider the problem of estimating the change point in the presence of right censoring and long-term survivors while using Kaplan-Meier estimator for the susceptible proportion. The maximum likelihood estimators are shown to be consistent. Taking one step further, we propose an counting process based and least squares based change-point detection algorithm. For single change-point case, consistency results are obtained. We then consider the detection of multiple change-points in the presence of long-term survivors via maximum likelihood based and counting process based method. Last but not least, we use a weighted least squares based and counting process based method for detection of multiple change-points with long-term survivors and covariates. For multiple change-points detection, simulation studies show good performances of our estimators under various parameters settings for both methods. All methods are applied to real data analyses. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

Nous présentons des inégalités fonctionnelles pour les processus ponctuels. Nous prouvons une inégalité de Sobolev logarithmique modifiée, une inégalité de Stein et un théorème du moment quatrième sans terme de reste pour une classe de processus ponctuels qui contient les processus binomiaux et les processus de Poisson. Les preuves reposent sur des techniques inspirées de l'approche de Malliavin-Stein et du calcul avec l'opérateur $Gamma$ de Bakry-Émery. Pour mettre en œuvre ces techniques nous développons une analyse stochastique pour les processus ponctuels. Plus généralement, nous mettons au point une théorie d'analyse stochastique sans hypothèse de diffusion. Dans le cadre des processus de Poisson ponctuels, l'inégalité de Stein est généralisée pour étudier la convergence stable vers des limites conditionnellement gaussiennes. Nous appliquons ces résultats pour approcher des processus Gaussiens par des processus de Poisson composés et pour étudier des graphes aléatoires. Nous discutons d'inégalités de transport et de leur conséquence en termes de concentration de la mesure pour les processus binomiaux dont la taille de l'échantillon est aléatoire. Sur un espace métrique mesuré quelconque, nous présentons un développement de la concentration de la mesure qui prend en compte l'agrandissement parallèle d'ensembles disjoints. Cette concentration améliorée donne un contrôle de toutes les valeurs propres du Laplacien métrique. Nous discutons des liens de cette nouvelle notion avec une version de la courbure de Ricci qui fait intervenir le transport à plusieurs marginales / We present functional inequalities and limit theorems for point processes. We prove a modified logarithmic Sobolev inequalities, a Stein inequality and a exact fourth moment theorem for a large class of point processes including mixed binomial processes and Poisson point processes. The proofs of these inequalities are inspired by the Malliavin-Stein approach and the $Gamma$-calculus of Bakry-Emery. The implementation of these techniques requires a development of a stochastic analysis for point processes. As point processes are essentially discrete, we design a theory to study non-diffusive random objects. For Poisson point processes, we extend the Stein inequality to study stable convergence with respect to limits that are conditionally Gaussian. Applications to Poisson approximations of Gaussian processes and random geometry are given. We discuss transport inequalities for mixed binomial processes and their consequences in terms of concentration of measure. On a generic metric measured space, we present a refinement of the notion of concentration of measure that takes into account the parallel enlargement of distinct sets. We link this notion of improved concentration with the eigenvalues of the metric Laplacian and with a version of the Ricci curvature based on multi-marginal optimal transport

In this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

[Truncated abstract] The multi-object filtering problem is a logical and fundamental generalization of the ubiquitous single-object vector filtering problem. Multi-object filtering essentially concerns the joint detection and estimation of the unknown and time-varying number of objects present, and the dynamic state of each of these objects, given a sequence of observation sets. This problem is intrinsically challenging because, given an observation set, there is no knowledge of which object generated which measurement, if any, and the detected measurements are indistinguishable from false alarms. Multi-object filtering poses significant technical challenges, and is indeed an established area of research, with many applications in both military and commercial realms. The new and emerging approach to multi-object filtering is based on the formal theory of random finite sets, and is a natural, elegant and rigorous framework for the theory of multiobject filtering, originally proposed by Mahler. In contrast to traditional approaches, the random finite set framework is completely free of explicit data associations. The random finite set framework is adopted in this dissertation as the basis for a principled and comprehensive study of multi-object filtering. The premise of this framework is that the collection of object states and measurements at any time are treated namely as random finite sets. A random finite set is simply a finite-set-valued random variable, i.e. a random variable which is random in both the number of elements and the values of the elements themselves. Consequently, formulating the multiobject filtering problem using random finite set models precisely encapsulates the essence of the multi-object filtering problem, and enables the development of principled solutions therein. '...' The performance of the proposed algorithm is demonstrated in simulated scenarios, and shown at least in simulation to dramatically outperform traditional single-object filtering in clutter approaches. The second key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on moment approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is also demonstrated in practical scenarios, and shown to considerably outperform traditional multi-object filtering approaches. The third key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on functional approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is compared with the previous, and shown to appreciably outperform the previous in certain classes of situations. The final key contribution is the definition of a consistent and efficiently computable metric for multi-object performance evaluation. It is shown that the finite set theoretic state space formulation permits a mathematically rigorous and physically intuitive construct for measuring the estimation error of a multi-object filter, in the form of a metric. This metric is used to evaluate and compare the multi-object filtering algorithms developed in this dissertation.

This thesis considers on the one hand the construction of point processes via conditional intensities, motivated by the partial Integration of the Campbell measure of a point process. Under certain assumptions on the intensity the existence of such a point process is shown. A fundamental example turns out to be the Pólya sum process, whose conditional intensity is a generalisation of the Pólya urn dynamics. A Cox process representation for that point process is shown. A further process considered is a Poisson process of Gaussian loops, which represents a noninteracting particle system derived from the discussion of indistinguishable particles. Both processes are used to define particle systems locally, for which thermodynamic limits are determined. / Betrachtet wird zum einen die Konstruktion von Punktprozessen mittels bedingter Intensitäten, motivert durch die partielle Integration des Campbell-Maßes eines Punktprozesses, die gerade bedingte Intensitäten liefert. Unter bestimmten Annahmen an die Intensitäten wird gezeigt, dass ein solcher Punktprozess existiert. Als ein fundamentaler Vertreter stellt sich der Pólyasche Summenprozess heraus, aus einer Verallgemeinerung der Dynamik der Pólyaschen Urne hervorgeht. Fuer ihn werden u.a. eine Darstellung als Cox-Prozess gezeigt. Mit einem Poissonprozess von Gaußschen Loops wird ein nicht wechselwirkendes Teilchensystem betrachtet, das aus der Diskussion von Systemen ununterscheidbarer Teilchen abgeleitet ist. Mit beiden Prozessen werden jeweils lokal Teilchensysteme konstuiert, fuer die die thermodynamischen Limiten identifiziert werden.

No description available.

In recent years, Inter Vehicle Communication (IVC) has become an intensive research area, as part of Intelligent Transportation Systems. It supposes that all, or a subset of the vehicles is equipped with radio devices, enabling communication between them. IEEE 802.11p (standardized for vehicular communication) shows a great deal of promise. By using ad hoc mode, this radio technology allows vehicles to extend their scopes of communication and thus forming a Multi-hop wireless Ad-hoc NETwork, also called Vehicular Ad-hoc NETwork (VANET). This thesis addresses a fundamental problem of VANET: the network capacity. Two simple theoretical models to estimate this capacity have been proposed: a packing model and a Markovian point process model. They offer simple and closed formulae on the maximum number of simultaneous transmitters, and on the distribution of the distance between them. An accurate upper bound on the maximum capacity had been derived. An analytical formula on distribution of the transmitters had been presented. This distribution allows us to optimize Clear Channel Assessment (CCA) parameters that leads to an optimization of the network capacity.In order to validate the approach of this thesis, results from the analytical models are compared to simulations performed with the network simulator NS-3. Simulation parameters was estimated from real experimentation. Impact of different traffic distributions (traffic of vehicles) on the network capacity is also studied. This thesis also focuses on extended perception map applications, which use information from local and distant sensors to offer driving assistance (autonomous driving, collision warning, etc.). Extended perception requires a high bandwidth that might not be available in practice in classical IEEE 802.11p ad hoc networks. Therefore, this thesis proposes an adaptive power control algorithm optimized for this particular application. It shows through an analytical model and a large set of simulations that the network capacity is then significantly increased.

The thesis investigates the concepts of archaeological spatial association within the context of both site and regional data sets. The techniques of geophysical surveying, surface distribution collection and aerial photography are described and discussed. Several new developments of technique are presented as well as a detailed discussion of the problems of data presentation and analysis. The quantitative relationships between these data sets are explored by modelling them as operands and describing association in terms of operators. Both local and global measures of association are considered with a discussion as to their relative merits. Methods for the spatial association of regional lattice and point processes are developed. A detailed discussion of distance based spatial analysis techniques is presented.

We study the minimum radius required for connectivity (CTR Critical Transmission Range) within homogeneous stationary Wireless Sensor Networks (WSN) topology control, considering different levels of attractivity within the sensors. Due to the complexity of dealing with this problem from a theoretical viewpoint, a Monte Carlo experience is devised for estimating the CTR distribution. With this information, we propose optimization procedures that, using as additional input a few known parameters (overall available budget, sensor cost, maximum available transmission radius, minimum probability of connectivity, environmental path loss and deployment cost) leads to the decision of the number and type of sensors to be acquired, their optimal communication radius and the ideal deployment strategy that maximize the WSN lifetime. As a previous result, the accuracy of several computational platforms for statistical computing was assessed, being the main conclusion that R (http://www.r-project.org) is the best choice / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresentamos a caracterização do raio de transmissão mínimo necessário para garantir conectividade, CTR (Critical Transmission Range), num cenário de controle de topologia em RSSF homogêneas e estacionárias. Dada a complexidade de se trabalhar com modelos analíticos, por meio de experiências Monte Carlo obtemos um estimador da distribuição do CTR sobre processos pontuais espaciais que descrevem o posicionamento dos nós sensores no ambiente para diferentes níveis de atratividade. Propomos modelos de otimização práticos que consideram diversos fatores conhecidos a priori pelo projetista como, por exemplo, os preços de diversos sensores, o raio de transmissão máximo disponível pelo sensor, os custos de posicionamento no ambiente (função da atratividade), o orçamento total do projeto, a probabilidade de conectividade mínima admissível e o exponente de path loss do ambiente. O modelo determina quais e quantos sensores devem ser comprados, com que raio de transmissão devem ser configurados e qual o preço conveniente a pagar pelo posicionamento (função da atratividade), para maximizar o tempo de vida de uma RSSF. Para guiar a escolha da plataforma de simulação e análise de dados, vários resultados a respeito de precisão numérica são apresentados, obtidos aplicando protocolos de avaliação já consolidados. Desta análise, determinamos que R (http://www.r-project.org) é a melhor escolha