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The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

Air pollution is an important determinant of health. There is convincing, and growing, evidence linking the risk of disease, and premature death, with exposure to various pollutants including fine particulate matter and ozone. Knowledge about the health and environmental risks and their trends is important stimulus for developing environmental and public health policy. In order to perform studies into the risks of environmental hazards on human health study there is a requirement for accurate estimates of exposures that might be experienced by the populations at risk. In this thesis we develop spatio-temporal models within a Bayesian framework to obtain accurate estimates of such exposures. These models are set within a hierarchical framework in a Bayesian setting with different levels describing dependencies over space and time. Considering the complexity of hierarchical models and the large amounts of data that can arise from environmental networks mean that inference using Markov Chain Monte Carlo (MCMC) may be computational challenging in this setting. We use both MCMC and Integrated Nested Laplace Approximations (INLA) to implement spatio-temporal exposure models when dealing with high–dimensional data. We also propose an approach for utilising the results from exposure models in health models which allows them to enhance studies of the health effects of air pollution. Moreover, we investigate the possible effects of preferential sampling, where monitoring sites in environmental networks are preferentially located by the designers in order to assess whether guideline and policies are being adhered to. This means the data arising from such networks may not accurately characterise the spatial-temporal field they intend to monitor and as such will not provide accurate estimates of the exposures that are potentially experienced by populations. This has the potential to introduce bias into estimates of risk associated with exposure to air pollution and subsequent health impact analyses. Throughout the thesis, the methods developed are assessed using simulation studies and applied to real–life case studies assessing the effects of particulate matter on health in Greater London and throughout the UK.

Following the pioneering work of Allenby and Ginter (1995) and Lenk et al.(1994); we propose in Section 2 a mixed effect model allowing for fixed and random effects as possible statistical solution to the problems mentioned above. Parameter estimation using a new, efficient variant of a Markov Chain Monte Carlo method will be discussed in Section 3 together with problems of model comparison techniques in the context of random effect models. Section 4 presents an application of the former to a brand-price trade-off study from the Austrian mineral water market. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this paper we head for a fully Bayesian analysis of the latent class model with a priori unknown number of classes. Estimation is carried out by means of Markov Chain Monte Carlo (MCMC) methods. We deal explicitely with the consequences the unidentifiability of this type of model has on MCMC estimation. Joint Bayesian estimation of all latent variables, model parameters, and parameters determining the probability law of the latent process is carried out by a new MCMC method called permutation sampling. In a first run we use the random permutation sampler to sample from the unconstrained posterior. We will demonstrate that a lot of important information, such as e.g. estimates of the subject-specific regression coefficients, is available from such an unidentified model. The MCMC output of the random permutation sampler is explored in order to find suitable identifiability constraints. In a second run we use the permutation sampler to sample from the constrained posterior by imposing identifiablity constraints. The unknown number of classes is determined by formal Bayesian model comparison through exact model likelihoods. We apply a new method of computing model likelihoods for latent class models which is based on the method of bridge sampling. The approach is applied to simulated data and to data from a metric conjoint analysis in the Austrian mineral water market. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

La mesure de la hauteur des océans, des vents de surface (fortement liés aux températures des océans), ou encore de la hauteur des vagues sont un ensemble de paramètres nécessaires à l'étude des océans mais aussi au suivi de leurs évolutions : l'altimétrie spatiale est l'une des disciplines le permettant. Une forme d'onde altimétrique est le résultat de l'émission d'une onde radar haute fréquence sur une surface donnée (classiquement océanique) et de la mesure de la réflexion de cette onde. Il existe actuellement une méthode d'estimation non optimale des formes d'onde altimétriques ainsi que des outils de classifications permettant d'identifier les différents types de surfaces observées. Nous proposons dans cette étude d'appliquer la méthode d'estimation bayésienne aux formes d'onde altimétriques ainsi que de nouvelles approches de classification. Nous proposons enfin la mise en place d'un algorithme spécifique permettant l'étude de la topographie en milieu côtier, étude qui est actuellement très peu développée dans le domaine de l'altimétrie. / After having scanned the ocean levels during thirteen years, the french/american satelliteTopex-Poséidon disappeared in 2005. Topex-Poséidon was replaced by Jason-1 in december 2001 and a new satellit Jason-2 is waited for 2008. Several estimation methods have been developed for signals resulting from these satellites. In particular, estimators of the sea height and wave height have shown very good performance when they are applied on waveforms backscattered from ocean surfaces. However, it is a more challenging problem to extract relevant information from signals backscattered from non-oceanic surfaces such as inland waters, deserts or ices. This PhD thesis is divided into two parts : A first direction consists of developing classification methods for altimetric signals in order to recognize the type of surface affected by the radar waveform. In particular, a specific attention will be devoted to support vector machines (SVMs) and functional data analysis for this problem. The second part of this thesis consists of developing estimation algorithms appropriate to altimetric signals obtained after reflexion on non-oceanic surfaces. Bayesian algorithms are currently under investigation for this estimation problem. This PhD is co-supervised by the french society CLS (Collect Localisation Satellite) (seehttp://www.cls.fr/ for more details) which will in particular provide the real altimetric data necessary for this study.

Neste trabalho analisa-se a relevância de saltos no apreçamento de derivativos de commodities através da comparação de dois modelos. O primeiro leva em consideração um convenience yield com reversão à média, enquanto o segundo é uma generalização do primeiro com saltos no preço à vista. Ambos os modelos são estimados por meio de uma abordagem Bayesiana, sendo as distribuições a posteriori simuladas com o uso de técnincas da família MCMC. Dados de petróleo, trigo e cobre são utilizados para fins de estimação. A análise econométrica indica significância estatística para saltos, mas não encontrou-se evidência significativa de que saltos melhoram o apreçamento de derivativos. / In this work we analyze the relevance of jumps in the pricing of commodity contingent claims by comparing two models. The first takes into account mean-reverting convenience yields, and the second is a generalization of the first with jumps in spot prices. Both models were estimated using a Bayesian approach, and posterior distributions where simulated using MCMC techniques. Oil, copper and wheat data where used for estimation proposes. Econometric analysis indicates statistical significance for jumps, but we found no strong evidence that jumps improve derivative pricing.

A assimetria de informação no sistema de saúde é um tema que ultrapassa o interesse apenas das empresas operadoras de seguro de saúde, de políticas públicas e de pesquisa acadêmica. O presente estudo analisa como os contratos de cosseguro influenciam os fenômenos do risco moral e da seleção adversa presentes nos planos de saúde e sua relação com a demanda de serviços médicos. Neste contexto, analisar a assimetria de informação no sistema de saúde se torna relevante por oferecer uma resposta consistente, que poderá embasar tanto as políticas públicas, quanto a forma de comercialização dos planos pelas empresas. Esse trabalho, a partir da Pesquisa Nacional por Amostra de Domicílios - PNAD 2003, procura observar a eficiência do contrato cosseguro como um mecanismo de mitigação de assimetria de informação, ou seja, excluídos os efeitos dos riscos associados ao indivíduo, se a diferença de contrato altera o comportamento dos agentes. Para atingir esse resultado foi proposto um método para testar a assimetria de informação utilizando o método de Monte Carlo. Os resultados sugerem que os contratos de cosseguros foram eficientes nos planos individuais, enquanto nos planos coletivos sua influência pode ser descartada. Por fim, o trabalho aponta que é mais eficiente, pelo bemestar social, a utilização de cosseguro para os contratos individuais, enquanto para os contratos coletivos são mais eficiente os contratos sem cosseguro. / Asymmetric information in the health care system is a topic of interest for medical insurance, policy makers and scholars. This research analyses how the contracts of coinsurance motivate the moral hazard and adverse selection phenomenon and consequences in medical services demand. In this context, the analysis of asymmetric information in the health care system provides support for the design of public policy and insurance plans. This research aims to estimate a structural model of health insurance and health care choices, using the 2003 National Household Sample Survey PNAD. It tested whether coinsurance contracts can work as efficient mechanisms to reduce risks related to asymmetric information. A methodological procedure using the Monte Carlo method was proposed to test for asymmetric information issues. The research suggests that coinsurance contracts were beneficial for individual plans, from a social welfare perspective. For the group plans, the benefit was not supported

In this paper we carry out fully Bayesian analysis of the general heterogeneity model, which is a mixture of random effects model, and its special cases, the random coefficient model and the latent class model. Our application comes from Conjoint analysis and we are especially interested in what is gained by the general heterogeneity model in comparison to the other two when modeling consumers' heterogeneous preferences. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In the present paper we study switching state space models from a Bayesian point of view. For estimation, the model is reformulated as a hierarchical model. We discuss various MCMC methods for Bayesian estimation, among them unconstrained Gibbs sampling, constrained sampling and permutation sampling. We address in detail the problem of unidentifiability, and discuss potential information available from an unidentified model. Furthermore the paper discusses issues in model selection such as selecting the number of states or testing for the presence of Markov switching heterogeneity. The model likelihoods of all possible hypotheses are estimated by using the method of bridge sampling. We conclude the paper with applications to simulated data as well as to modelling the U.S./U.K. real exchange rate. (author's abstract) / Series: Forschungsberichte / Institut für Statistik