STOCHASTIC PROCESSES

Author: LÓPEZ SANJUÁN EVA TERESA.
Year: 2004.
University: EXTREMADURA [www.unex.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This doctoral thesis falls within the framework of the theory of reliability and the theory of stochastic processes. This paper presents a new stochastic process, the so-called potential, which allows modeling of operational time and / or repair of a system in decay. For this process stochastic explores its major properties, especially those related to convergence, orders and classes of stochastic aging. The second part of this thesis is devoted to the study of a new policy of keeping repairable systems that is based on the concept of reparations proposal. The main idea behind this policy is that the repair of failures suffered by the system was postponed until a time when the repair is less costly. This policy of keeping it comes under two models. For both models, analyzes the expected benefit by working period in order to determine the optimal compensation policy. Similarly, the theoretical results are illustrated with numerical examples.

Author: GUTIÉRREZ SÁNCHEZ RAMÓN.
Year: 2004.
University: GRANADA [www.ugr.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: UNIVERSIDAD DE GRANADA.

Summary: The most significant contributions of this thesis are: 1 - are set in a definitive way, the theory and probabilistic inference about their parameters, a model Dissemination Lognormal, multivariate not homogeneous with exogenous factors own for each endogenous variable ( Chapter 2), showing its potential for the stochastic modeling of actual two-dimensional phenomena (GDP price dela new home in Spain, Chapter 5). 2, - is studied, probabilistic and statistically, several models broadcasts unviariantes not homogeneous with exogenous factors functional, suitable for cases of special interest in the theory Times First Step (Chapter 4). 3 - Several models are considered type Gomertz, homogeneous and not homogeneous with exogenous factors and general functional factors observed in discrete time. Established by statistical inference with continuous sampling factors observed quietly, and provides examples of their use in modeling the evolution of trends in vehicle fleet in Spain, as fuel (Chapter 6). 4, - completes the study probability of the Spread of Rayleigh, univariate and homogeneous, and provides basic statistical inference on its parameters through continuous sampling. It applies to real cases of concern, analyzing trends in life expectancy at birth and infant mortality, among others, in Andalusia and Spain.

Author: RAMOS ÁBALOS EVA M..
Year: 2004.
University: GRANADA [www.ugr.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: Starting with the study of distributions lognormales triparamétricas, is considered the original study of diffusion processes lognormales triparamétricos multidimensional. In a first phase study the case without exogenous factors, and then extends to the case of exogenous factors that affect all endogenous variables. It begins by focusing our study on the process of three-dimensional lognormal parameters, introducing the process from the point of view of the solution of the equations of Kolmogorov. It defines the model identifies the points in the process and deals with the estimation of parameters. From here, there are two methods for the simulation of the track record and is planted to a reparameterization process (Chapter 1). Then we focused on the study of two-dimensional lognormal process with three parameters that exogenous factors affecting their trend. The reason that leads to the introduction of exogenous factors, is that it describes the continuing trend of certain phenomena dynamic, drawing on his observation discreet. In this way, you can enter an explanation of the behavior of an array of variables based on another set of independent variables that affect those, and whose evolution over time is known. As in the first chapter, presents that process from the point of view of the solution of the equations of Kolmogorov. Identify points in the process, deals with the estimation of the parameters and other calculating the information matrix Fisher (Chapter 2). He then introduced the three dimensional lognormal process parameters and exogenous factor, so that each component of the vector exogenous affect the endogenous variable corresponding to the trend intestinal process, using the equation of forward and backward Kolmogorov. The model is developed from the basic model with multiple exogenous factors that affect all endogenous variables. Obviously, the model proposed here can not developers as of the particular case cited, offsetting the respective coefficients in each component, and therefore need a thorough development. To this end, establishing the Kolmogorov equations and the corresponding two-dimensional density transition. We determine the time, it is proposed to estimate maximum credible parameters based on a pattern of discrete sampling (Chapter 3). Further development of a multi-dimensional extension to the case of the second chapter, ie defines the process logarithmic normal multidimensional three parameters with exogenous factors in the trend of the process, using the equation of forward and backward Kolmogorov. It determines the information matrix Fisher and also presents some contrast based on the rate of versoimilitudes (Chapter 4). Finally an application is made to real data. First, the methodology used in the process of diffusion lognormal dimensional triparamétrico presented in the first chapter, for the study of the evolution of a basic demographic indicator is the marriage, namely the variable "Mean age at first marriage in Spain and Autonomous Community of Andalusia. Secondly, the method is planted and optimization "Simulated Annealing." This method is described and then applied to different data sets. The application is first on the sets of simulated data to verify that the method is effective, then all four groups of real data used in this chapter. Shown together with the results obtained by the method of maximum likelihood allowing a comparison of the two (Chapter 5)

Author: RICO CASTRO NURIA.
Year: 2004.
University: GRANADA [www.ugr.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In this report, structured into three chapters, it is essentially two questions on the process of diffusion lognormal: building trust and bands of the case study that exogenous factor is a polynomial. The first chapter describes the results of the process of diffusion and lognormal provides three different methods for obtaining this process. The second chapter of the report addresses the problem of building confidence bands for the middle and fashion features of the process of diffusion of roughly lognormal and widespread, explores various methods of construction and these bands are compared using simulation in terms errors coverage, mean amplitude, etc.. Third is a study of the process of diffusion lognormal with exogenous factors - type polynominal case which is of particular interest when there is no information on sample external variables that may

Author: Martínez Beneito Miguel Ángel.
Year: 2005.
University: VALENCIA [www.uv.es].
Place of defense: Facultad de Matemáticas.
Place of preparation: Facultad de ciencias matemáticas.

Summary: The determination of geographical aggregations in the incidence of certain disease is a problem of great tradition in epidemiology and statistics in which space has devoted great efforts. This situation is compounded when the number of existing aggregations is unknown and probably greater than 1 and the location of the pockets of risk is unknown. This paper deals with the detection of outbreaks of statistical risk outbreaks. The detection is based on the study of the location of the addresses of the cases that have been involved in outbreaks. The proposed model is based on the study of these addresses using techniques timely processes, in particular the models Cox log-Gaussianos, and the processes of mixtures with an undetermined number of components. The inference on this model takes place within the Bayesian framework, using simulation MCMC. In this thesis, in addition to propose a model for determining the number of outbreaks, comparing their results compared with the implementation of model mixtures with an undetermined number of components for the detection of outbreaks in outbreaks. Moreover, once rated the benefits of modeling proposal will apply to the detection of outbreaks of risk they have been able to intervene in outbreaks of legionellosis that have happened in the city of Alicante Alcoi from September 1999 to November 2003.

Author: VALVERDE CASTILLO SERGI.
Year: 2005.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: AULA MASTER, EDIFICI A-3-CAMPUS NORD.
Place of preparation: EDIFICI B5 DESPATX B5-011 NORD.

Author: ROMERO MOLINA DESIRÉE.
Year: 2005.
University: GRANADA [www.ugr.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In this dissertation is proposed and studied a new process for disseminating associated with a particular expression of the growth curve type Gompertz which makes the upper curve of that depends on the initial value at the moment. There has been, first, a historical summary of the main models for growth, focusing on some of the existing stochastic processes associated with major growth curves (Chapter 1). Then work has been obtaining the new process we are proposing and the study of its main features (Chapter 2). To continue to raise the estimation of the model by providing alternative methods for obtaining the estimators because of the difficulties that pose. Also included is a study of the problem of time first-pass passage through barriers and a study of the problem of the time it occurs in the watershed model (Chapter 3). Finally, apply the results obtained over the memory to real data. In particular fits a model of the type proposed to data previously submitted to motivate the introduction of new process proves the usefulness of it. It also proposes a strategy to find groups with similar behavioral patterns (Chapter 4).

Author: SANTAMARÍA NAVARRO CRISTINA.
Year: 2005.
University: POLITÉCNICA DE VALENCIA [www.upv.es].
Place of defense: Dep. Matematica Aplicada.
Place of preparation: Universidad Politécnica de Valencia.

Summary: In this paper detailing the process of constructing a mathematical model to predict recurrence after excision of the tumor, superficial bladder carcinoma (stadiums Ta, T1), using standard clinical factors and clearly defined in the medical literature. The methodology was developed in the context of the processes of counting and theory martingalas. It starts with a non - parametric analysis of the database, which provides an initial approach to the prognostic factors of the risk of recurrence. After quantified the relationship between these factors and joint experience of survival (no relapse) of a patient through the model of Cox proportional hazards, and there is a model to predict the risk of first recurrence over time. This result is complemented with the approach of censure by intervals, using a model due to Farrington. Through extensions Cox model incorporates information from multiple relapses, reaching a hybrid model Prentice-Williams-Peterson/Andersen-Gill as the most suitable to our data. Based on the modeling construct nomogramas, which provide a graphical and easy to doctor and patient to decide the protocol for monitoring and treatment more appropriate to the situation of his illness.

Author: SALMERON MARTINEZ DIEGO.
Year: 2006.
University: MURCIA [www.um.es].
Place of defense: FACULTAD DE MATEMATICAS.
Place of preparation: FACULTAD DE MATEMATICAS.

Summary: The problem of choice of the a priori distribution, both for problems estimation problems for selecting models or assumptions contrast, is one of the major problems that one faces when deciding goal Bayesian analysis. Moreover, increasingly, in statistical parametric models have an increased complexity to the point of not being able to be evaluated depending on the likelihood associated with a given data set. This is the case of diffusion models, whose applications to fields as diverse as finance, engineering, make their study as necessary. The author of the thesis deals with the two previous problems getting theoretical results, proposing new methodologies and numerous examples. On the one hand, in Chapter 2, it shows the potential weaknesses that a classical inference based on maximum likelihood estimator can have and the benefits of treatment with Bayesian distributions ante default or objective, in trouble with restrictions on the parameters, in particular, a model that explains the proportion of the area degraded over time. In chapter 3, proposing a priori integral distributions for the selection of Bayesian models, and chapters 4 and 5 are dedicated to the implementation of the schemes of Euler and methods of particle filter and missing data in diffusion processes . Distributions a priori integral proposed as a solution to the problem of uncertainty factor Bayes. This uncertainty appears when using a priori distributions by default or not informative (improper), as they are defined except for a constant of proportionality, meaning that Bayes factor is undefined. Distributions a priori integral said no problems have properties very interesting tion from the point of view of theory and practical and have a close relationship with the theory of Markov chains. Schemes for Euler diffusion processes are widely used to approximate the distribution afterwards. The thesis demonstrates for the first time that the approximations are convergent and there is the speed of convergence. In this type of stochastic processes (diffusion processes), Monte Carlo methods and Markov chains, but very used to make Bayesian inference, have the disadvantage of having a very slow speed of convergence as the Markov chains that appear likely not to be irreducible. The methods of particle filter and missing data is proposed as an alternative to Monte Carlo methods and Markov chains for inference in stochastic processes related to the diffusion processes.

Author: DIEHL FRANK.
Year: 2006.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: AULA MASTER- EDIFICI A3- CAMPUS NORD.
Place of preparation: D4 205 Nord.

Summary: This thesis studies the definition, implementation and validation of multilingual and crosslingual acoustic models for automatic speech recognition (ASR). The acoustic model constitutes one of the basic building blocks of an automatic speech recognition system. In today's state-of-the-art ASR systems it is common practise to extract the parameters of the acoustic model from a acoustic template database. It has been shown that this methodology results in high performance ASR systems. However, a principal drawback of this procedure consist in its dependency on suitable speech databases to train the models, and the inevitable dependency of the final target system on the language used for training the models. That is, in case of acoustic model training, a acoustic model can hardly be build if no or only a limited amount of speech material of a target language is available, and, during recognition, the ASR system is fixed to the language which was used to train it. Multilingual and crosslingual acoustic modelling is seen as a potential way to overcome these drawbacks at least partly. The basic idea consists in sharing acoustic knowledge between languages, or to reuse already available acoustic knowledge from one or more source languages for a target language. The thesis on hand thus focuses on two major aspects of multilingual and crosslingual acoustic modelling: acoustic model definition and acoustic model adaptation. In case of acoustic model definition the stress lies on the definition of suitable linguistic features. Linguistic features constitute the input domain of the phonetic-acoustic decision tree which is used to define context dependent acoustic models. Usually such features are derived knowledge-based by a linguistic expert which is familiar with both, the source and the target language. However, linguistic experts which are familiar with all concerned languages might be hard to find. Thus, in a multilingual but also in the crosslingual environment, this approach is at least to some degree questionable. To overcome the described problem, in this work we examine a novel data-driven approach to obtain such features. We show that the obtained so-called âLocal Codebook Featuresâ (LCB) bear the desired linguistic information content, and we apply them to various multilingual and crosslingual tasks. With respect to crosslingual acoustic model adaptation, in this thesis two different kinds of adaptation schemes were developed. We have investigated the adaptation of the phonetic-acoustic decision tree by means of so-called 'polyphone decision tree specialisation' (PDTS), and acoustic model adaptation of the original and of the re-generated acoustic model sets. In case of the acoustic models we focus on the use of semicontinuous hidden Markov models. A novel model adaptation scheme is introduced, acting on the mixture weights associated to the prototype densities of the codebooks. Depending on the applied optimisation scheme, two adaptation methods were obtained which we call maximum likelihood convex regression (MLCR) and maximum a posteriori convex regression (MAPCR). For two crosslingual acoustic modelling tasks, using multilingual Spanish-English-German source models for the target languages Slovenian and French, it was shown that the combination of PDTS with MAPCR tends to outperform other adaptation schemes clearly.

Author: CUADRAS PALLEJÀ DANIEL.
Year: 2006.
University: BARCELONA [www.ub.es].
Place of defense: FACULTAD DE BIOLOGÍA.
Place of preparation: FACULTAD DE BIOLOGÍA.

Summary: This report deals with the generalization of classical techniques of analysis Multivariante discreet, especially the Principal Component Analysis and Correspondence Analysis. It was divided into two parts, plus an appendix containing a summary in English. In the first part, was spreading the concept of Major Components of an array of discrete data, in case of a continuous random variable and focused stochastic process associated with it. By Mathematical analysis results concerning the spectral decomposition of a symmetric kernel, applied to the nucleus of covariance process, we obtain a set of standard variables compound, called Main Directions of properties similar to the Principal Component of discrete event. Additional results are also studying on the subject, as theorems of expanding core of covariance, methods of obtaining the Main Directions by resolution of a differential equation, formulas for the expression of covariance functions between random variables, and some inequities and series on the Main Directions and covariance. The second part discusses the relationship between the correlation analysis, and alternative based on the distance of Hellinger, as methods to study the relationship between two categorical variables tabulated in a correlation matrix. The analysis of the process that leads to another technique allows us to propose a new alternative, the Correspondence Analysis Paramétrico, which includes the two previous techniques such as cases for the extreme values of this parameter. We studied the relationship of this new technique with a distance, a measure of comparison with the Correspondence Analysis, the concept of geometric variability and tests of independence, and two methods to establish the optimal parameter value as our goals. We also propose a generalization of this technique to discrete event of a bivariate vector absolutely continuous, both from the point of view as a classic with the new parametric approach that we proposed. The main conclusion of this report is that it is possible to generalize Technical Analysis Multivariante unobtrusive to the case continued, using the same continuum all necessary discrete processes.

Author: SUREDA CARBONELL BARBARA.
Year: 2006.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: Sala de Conferències de l'EUETIT.

Summary: Modern cities are characterised by progressive population growth in limited physical spaces. This growth gives rise to many problems, including lack of self-containment of cities, spatial segregation of heterogeneous population sectors (whether for economic, social or cultural reasons), the collapse of transport infrastructures, and the lack of green areas. The aim of this doctoral thesis is to facilitate the analysis of a system’s sustainability. It examines a particular urban system and puts forward a methodology for analysing the sustainability of urban systems that can be applied to medium-size European towns. The methodology proposed is based on a three-part conceptual framework. Firstly, sustainable development can only be applied through a systematic, transversal and multidisciplinary approach. Secondly urban systems must be considered as being inherently complex, as they are made up of multiple interrelationships between their component parts, which in turn interact with their surroundings. This complexity means that the systems are faced with enormous challenges at all levels, and may even face collapse. Thirdly, one of the features that must be taken into account in dealing with complex systems is their high level of uncertainty. The proposed methodology is based on this conceptual framework and a review of existing tools for measuring and modelling sustainability. The result is a process based on a set of tools (models, correlations between variables, indicators, indices and future scenarios) that can be used to analyse urban systems characterised by specific problems and to define strategies and policies for achieving sustainable development in these systems. Through the application of the methodology to a specific case study, the municipality of Terrassa, it was possible to identify problems that may have a significant impact on the town’s sustainable development and to define suitable strategies for achieving urban containment.

Author: VIDAL CALLEJA TERESA ALEJANDRA.
Year: 2006.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: Sala d'Actes Facu. de Matemà.i Estad..
Place of preparation: EDIFICI U DESPATX 518 Campus SUD.

Summary: Navigation in mobile robotics involves two tasks, keeping track of the robot's position and moving according to a control strategy. In addition, when no prior knowledge of the environment is available, the problem is even more difficult, as the robot has to build a map of its surroundings as it moves. These three problems ought to be solved in conjunction since they depend on each other. This thesis is about simultaneously controlling an autonomous vehicle, estimating its location and building the map of the environment. The main objective is to analyse the problem from a control theoretical perspective based on the EKF-SLAM implementation. The contribution of this thesis is the analysis of system's properties such as observability, controllability and stability, which allow us to propose an appropriate navigation scheme that produces well-behaved estimators, controllers, and consequently, the system as a whole. We present a steady state analysis of the SLAM problem, identifying the conditions that lead to partial observability. It is shown that the effects of partial observability appear even in the ideal linear Gaussian case. This indicates that linearisation alone is not the only cause of SLAM inconsistency, and that observability must be achieved as a prerequisite to tackling the effects of linearisation. Additionally, full observability is also shown to be necessary during diagonalisation of the covariance matrix, an approach often used to reduce the computational complexity of the SLAM algorithm, and which leads to full controllability as we show in this work. Focusing specifically on the case of a system with a single monocular camera, we present an observability analysis using the nullspace basis of the stripped observability matrix. The aim is to get a better understanding of the well known intuitive behaviour of this type of systems, such as the need for triangulation to features from different positions in order to get accurate relative pose estimates between vehicle and camera. Through characterisation the unobservable directions in monocular SLAM, we are able to identify the vehicle motions required to maximise the number of observable states in the system. When closing the control loop of the SLAM system, both the feedback controller and the estimator are shown to be asymptotically stable. Furthermore, we show that the tracking error does not influence the estimation performance of a fully observable system and viceversa, that control is not affected by the estimation. Because of this, a higher level motion strategy is required in order to enhance estimation, specially needed while performing SLAM with a single camera. Considering a real-time application, we propose a control strategy to optimise both the localisation of the vehicle and the feature map by computing the most appropriate control actions or movements. The actions are chosen in order to maximise an information theoretic metric. Simulations and real-time experiments are performed to demonstrate the feasibility of the proposed control strategy.