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The thesis proposes management options and risk minimizing in the field of building materials production technologies and related products using fuzzy logic and other risk management tools. The thesis indicates why some methodologies are not commonly used. The main purpose of this work (thesis) is to propose possible upgrades of standard methods in process capability and risk minimizing related to building materials and products. Markov analysis and fuzzy Markov chains are applied.

Cancer as a disease causes about 8.8 million deaths worldwide per year, a number that will largely increase in the next decades. Although the cellular processes involved in tumor emergence are more and more understood, the implications of specific changes at the cellular scale on tumor emergence at the tissue scale remain elusive. Main reasons for this lack of understanding are that the cellular processes are often hardly observable especially in the early phase of tumor development and that the interplay between cellular and tissue scale is difficult to deduce. Cell-based mathematical models provide a valuable tool to investigate in which way observable phenomena on the tissue scale develop by cellular processes. The implications of these models can elucidate underlying mechanisms and generate quantitative predictions that can be experimentally validated. In this thesis, we infer the role of genetic and phenotypic cell changes on tumor development with the help of cell-based Markov chain models which are calibrated by tissue-scale data. In the first part, we utilize data on the diagnosed fractions of benign and malignant tumor subtypes to unravel the consequences of genetic cell changes on tumor development. We introduce extensions of Moran models to investigate two specific biological questions. First, we evaluate the tumor regression behavior of pilocytic astrocytoma which represents the most common brain tumor in children and young adults. We formulate a Moran model with two absorbing states representing different subtypes of this tumor, derive the absorption probabilities in these states and calculate the tumor regression probability within the model. This analysis allows to predict the chance for tumor regression in dependency of the remaining tumor size and implies a different clinical resection strategy for pilocytic astrocytoma compared to other brain tumors. Second, we shed light on the hardly observable early cellular dynamics of tumor development and its consequences on the emergence of different tumor subtypes on the tissue scale. For this purpose, we utilize spatial and non-spatial Moran models with two absorbing states which describe both benign and malignant tumor subtypes and estimate lower and upper bounds for the range of cellular competition in different tissues. Our results suggest the existence of small and tissue-specific tumor-originating niches in which the fate of tumor development is decided long before a tumor manifests. These findings might help to identify the tumor-originating cell types for different cancer types. From a theoretical point of view, the novel analytical results regarding the absorption behavior of our extended Moran models contribute to a better understanding of this model class and have several applications also beyond the scope of this thesis. The second part is devoted to the investigation of the role of phenotypic plasticity of cancer cells in tumor development. In order to understand how phenotypic heterogeneity in tumors arises we describe cell state changes by a Markov chain model. This model allows to quantify the cell state transitions leading to the observed heterogeneity from experimental tissue-scale data on the evolution of cell state proportions. In order to bridge the gap between mathematical modeling and the analysis of such data, we developed an R package called CellTrans which is freely available. This package automatizes the whole process of mathematical modeling and can be utilized to (i) infer the transition probabilities between different cell states, (ii) predict cell line compositions at a certain time, (iii) predict equilibrium cell state compositions and (iv) estimate the time needed to reach this equilibrium. We utilize publicly available data on the evolution of cell compositions to demonstrate the applicability of CellTrans. Moreover, we apply CellTrans to investigate the observed cellular phenotypic heterogeneity in glioblastoma. For this purpose, we use data on the evolution of glioblastoma cell line compositions to infer to which extent the heterogeneity in these tumors can be explained by hierarchical phenotypic transitions. We also demonstrate in which way our newly developed R package can be utilized to analyze the influence of different micro-environmental conditions on cell state proportions. Summarized, this thesis contributes to gain a better understanding of the consequences of both genetic and phenotypic cell changes on tumor development with the help of Markov chain models which are motivated by the specific underlying biological questions. Moreover, the analysis of the novel Moran models provides new theoretical results, in particular regarding the absorption behavior of the underlying stochastic processes.

Hidden Markov Models (HMMs) have seen widespread use in a variety of applications ranging from speech recognition to gene prediction. While developed over forty years ago, they remain a standard tool for sequential data analysis. More recently, Latent Dirichlet Allocation (LDA) was developed and soon gained widespread popularity as a powerful topic analysis tool for text corpora. We thoroughly develop LDA and a generalization of HMMs and demonstrate the conjunctive use of both methods in predictive data analysis for health care problems. While these two tools (LDA and HMM) have been used in conjunction previously, we use LDA in a new way to reduce the dimensionality involved in the training of HMMs. With both LDA and our extension of HMM, we train classifiers to predict development of Chronic Kidney Disease (CKD) in the near future.

[pt] Finanças corporativas compreendem políticas de investimento, financiamento e dividendo cujo objetivo é maximizar o valor do acionista. Em particular, os resultados de empresas produtoras de commodities e, consequentemente, o valor para seus acionistas estão sujeitos a alta volatilidade, decorrentes da variação dos preços destes produtos no mercado global. Entretanto, o risco dessa variação pode ser mitigado ao se explorar o amplo mercado de derivativos que, em geral, está disponível para commodities. Este trabalho propõe calcular o acréscimo de valor que uma empresa produtora de commodities pode fornecer ao seu acionista pelo uso de uma política ótima de gestão de derivativos, por meio da compra ou venda de contratos a termo. Para tanto, busca maximizar o retorno aos acionistas via dividendos em um ambiente avesso a risco. O modelo assume que o preço da commodity segue um processo de Markov de estados discretos. Como o modelo é aplicado em vários estágios, o problema torna-se bastante complexo, sendo necessário usar um método de decomposição para obter a solução, sendo assim, utilizou-se o método conhecido como programação dual dinâmica estocástica. Os resultados demonstram que, ao comercializar contratos forward, uma empresa aumenta o valor percebido pelo acionista, medido pelo pagamento de dividendos, para qualquer nível de aversão a risco. A média de acréscimo de valor, considerando diferentes níveis de aversão a risco e uma premissa de precificação não viesada, é superior a 320 por cento quando comparado a empresas que não possuem acesso a tais instrumentos. Além de medir o acréscimo de valor, analisou-se também quais os fatores determinantes para a política ótima de gestão de derivativos. Foi possível identificar que a política de gestão de derivativos é muito determinada pelos preços, que por sua vez estão associados ao estado da cadeia de Markov vigente em cada estágio. / [en] Corporate finance comprises investment, financing and dividend policies aimed at maximizing shareholder value. In particular, the results of commodity producers and, consequently, the value to their shareholders are subject to high volatility, resulting from the variation of prices of these products in the global market. However, the risk of this variation can be mitigated by exploiting the broad derivatives market that is generally available for commodities. This work proposes to calculate the value increase that a commodity-producing company can provide to its shareholders through the use of an optimal derivatives management policy, by buying or selling forward contracts. To this end, it seeks to maximize shareholder returns via dividends in a risk-averse environment. The model assumes that the commodity price follows a discrete state Markov process. Since the model is applied in several stages, the problem becomes quite complex, and it is necessary to use a decomposition method to obtain the solution, so we used the method known as stochastic dynamic dual programming. The results show that by trading forward contracts, a company increases the value perceived by the shareholder, measured by the payment of dividends, to any level of risk aversion. The average value increase, considering different levels of risk aversion and an unbiased pricing assumption, is higher than 320 per cent when compared to companies that do not have access to such instruments. In addition to measuring the value increase, we also analyzed which factors determine the optimal derivatives management policy. It was possible to identify that the derivatives management policy is very determined by the prices, which in turn are associated with the state of the Markov chain in force at each stage.

In quantified safety engineering, mathematical probability models are used to predict the risk of failure or hazardous events in systems. Markov processes have commonly been utilized to analyze the safety of systems modeled as discrete-state stochastic processes. In continuous time Markov models, transition time between states are exponentially distributed. Semi-Markov processes expand this modeling framework by allowing transition time between states to follow any distribution. This master thesis project seeks to extend the semi-Markov modeling framework even further by allowing hierarchical states, which further relaxes Markov-assumptions by allowing models to keep memory even in state transition. To achieve this, the master thesis proposes a method using the phase-type distribution to replace Markov-chains of states to a single state. For application purposes, it is shown how semi-Markov chains with phase-type distributed transitions can be evaluated by a method using the Laplace-Stieltjes transform. Furthermore, to replace semi-Markov chains, a method to approximate these by the phase-type distribution is presented. This is done by deriving the moments of the time to absorption in a semi-Markov process with a method using the Laplace-Stieltjes transform, and fitting a phase-type distribution with these moments. To evaluate the methods, some case studies are performed on appropriate models. Analytical results are compared with Monte-Carlo simulations and Laplace-transform inverse methods. The results are used to show how hierarchical semi-Markov models can be replaced in an exact manner, and how semi-Markov models can be replaced approximately with varying accuracy. An important conclusion is that by enabling hierarchical modeling, it is possible to predict the safety of systems which demand a more realistic model, as relaxing Markov assumptions allows for more complexity. / Matematiska sannolikhetsmodeller används inom kvantifierad säkerhetsteknik för att utvärdera risken för fel eller farliga olyckor i system. Ett vanligt sätt att analysera säkerheten i system som kan modelleras som stokastiska processer med diskreta tillstånd är att använda Markovprocesser. I tidskontinuerliga Markovprocesser är tidsövergången mellan tillstånd exponentialfördelade. Semi-Markov processer utökar denna modelleringsteknik ytterligare genom att tillåta tidsövergångar som är fördelade enligt alla möjliga fördelningar. Detta examensarbete har som mål att utöka modelleringsmöjligheterna med Semi-Markov processer genom att tillåta hierarkiska tillstånd, som därmed ytterligare utmanar antaganden inom Markov-modeller genom att bibehålla minne efter tillståndsövergång. För att uppnå detta föreslås i denna rapport en metod som använder phase-type-fördelningen för att byta ut Markovkedjor med ett enda tillstånd. För att tillämpa metoden visas hur semi-Markov kedjor kan utvärderas med hjälp av Laplace-Stieltjes-transformen. För att kunna ersätta semi-Markov kedjor med samma metod presenteras även en approximationsmetod för att åter igen använda phase-type-fördelningen. Detta görs genom att använda Laplace-Stieltjes-transformen för att generera momenten av tiden till absorption i semi-Markov processer, och anpassa dessa till momenten av en phase-type-fördelning. För att utvärdera metoderna presenteras en del exempel. Analytiska resultat jämförs med Monte-Carlo simulering och inverteringsmetoder för Laplace-transformen. Resultaten används för att visa hur hierarkiska Markov modeller kan ersättas exakt, och hur semi-Markov processer kan approximeras med varierande noggrannhet. En viktig slutsats är att genom att tillåta hierarkisk modellering är det möjligt att utvärdera säkerheten i system som kräver mer realistiska modeller, då detta öppnar upp för mer komplexitet.

[pt] O aumento da participação de fontes de energias renováveis variáveis (ERVs) na matriz elétrica do Brasil traz diversos desafios ao planejamento e à operação do Sistema Elétrico Brasileiro (SEB), devido à estocasticidade das ERVs. Tais desafios envolvem a modelagem e simulação dos processos intermitentes de geração e, dessa forma, um volume considerável de pesquisas tem sido direcionado ao tema. Nesse contexto, um tópico de crescente importância na literatura relaciona-se ao desenvolvimento de metodologias para simulação estocástica conjunta de recursos intermitentes com características complementares, como, por exemplo, as fontes eólica e solar. Visando contribuir com essa temática, este trabalho propõe melhorias a um modelo de simulação já estabelecido na literatura, avaliando sua aplicabilidade a partir de dados do Nordeste brasileiro. A metodologia proposta baseia-se em discretização das séries temporais de energia aplicando a técnica de machine learning k-means, construção de matrizes de transição de estados com base nos clusters identificados e simulação de Monte Carlo para obtenção dos cenários. As séries sintéticas obtidas são comparadas aos resultados gerados pelo modelo já estabelecido na literatura a partir de técnicas estatísticas. Quanto ao alcance dos objetivos da pesquisa, a modelagem proposta se mostrou mais eficiente, gerando cenários que reproduziram satisfatoriamente todas as características dos dados históricos avaliadas. / [en] The increased participation of variable renewable energy sources (VRES) in Brazil s electricity matrix brings several challenges to the planning and operation of the Brazilian Power System (BPS), due to the VRES stochasticity. Such challenges involve the modeling and simulation of intermittent generation processes and, in this context, a considerable amount of research has been directed to the theme. In this context, a topic of increasing importance in the literature is related to the development of methodologies for joint stochastic simulation of intermittent resources with complementary characteristics, such as wind and solar sources. Aiming to contribute to this theme, this work proposes improvements in a simulation model already established in the literature, evaluating its applicability based on Brazilian Northeast data. The proposed methodology is based on the discretization of energy time series applying the kmeans machine learning technique, construction of state transition matrices based on the identified clusters, and Monte Carlo simulation to obtain the scenarios. The synthetic series obtained are compared to the results generated by the model already established in the literature from statistical techniques. Regarding the scope of the research objectives, the proposed modeling demonstrated more promising results, generating scenarios that satisfactorily reproduced all the evaluated characteristics of the historical data.

Being one of the fastest growing fields of engineering, wireless has gained the attention of researchers and commercial businesses all over the world. Extensive research is underway to improve the performance of existing systems and to introduce cutting edge wireless technologies that can make high speed wireless communications possible. The first part of this dissertation deals with discrete channel models that are used for simulating error traces produced by wireless channels. Most of the time, wireless channels have memory and we rely on discrete time Markov models to simulate them. The primary advantage of using these models is rapid experimentation and prototyping. Efficient estimation of the parameters of a Markov model (including its number of states) is important to reproducing and/or forecasting channel statistics accurately. Although the parameter estimation of Markov processes has been studied extensively, its order estimation problem has been addressed only recently. In this report, we investigate the existing order estimation techniques for Markov chains and hidden Markov models. Performance comparison with semi-hidden Markov models is also discussed. Error source modeling in slow and fast fading conditions is also considered in great detail. Cognitive Radio is an emerging technology in wireless communications that can improve the utilization of radio spectrum by incorporating some intelligence in its design. It can adapt with the environment and can change its particular transmission or reception parameters to execute its tasks without interfering with the licensed users. One problem that CR network usually faces is the difficulty in detecting and classifying its low power signal that is present in the environment. Most of the time traditional energy detection techniques fail to detect these signals because of their low SNRs. In the second part of this thesis, we address this problem by using higher order statistics of incoming signals and classifying them by using the pattern recognition capabilities of HMMs combined with cased-based learning approach. This dissertation also deals with dynamic spectrum allocation in cognitive radio using HMMs. CR networks that are capable of using frequency bands assigned to licensed users, apart from utilizing unlicensed bands such as UNII radio band or ISM band, are also called Licensed Band Cognitive Radios. In our novel work, the dynamic spectrum management or dynamic frequency allocation is performed by the help of HMM predictions. This work is based on the idea that if Markov models can accurately model spectrum usage patterns of different licensed users, then it should also correctly predict the spectrum holes and use these frequencies for its data transmission. Simulations have shown that HMMs prediction results are quite accurate and can help in avoiding CR interference with the primary licensed users and vice versa. At the same time, this helps in sending its data over these channels more reliably. / Ph. D.

Cette thèse se décompose en deux parties. Dans un premier temps nous nous intéressons à la sélection bayésienne de variables dans un modèle probit mixte.L'objectif est de développer une méthode pour sélectionner quelques variables pertinentes parmi plusieurs dizaines de milliers tout en prenant en compte le design d'une étude, et en particulier le fait que plusieurs jeux de données soient fusionnés. Le modèle de régression probit mixte utilisé fait partie d'un modèle bayésien hiérarchique plus large et le jeu de données est considéré comme un effet aléatoire. Cette méthode est une extension de la méthode de Lee et al. (2003). La première étape consiste à spécifier le modèle ainsi que les distributions a priori, avec notamment l'utilisation de l'a priori conventionnel de Zellner (g-prior) pour le vecteur des coefficients associé aux effets fixes (Zellner, 1986). Dans une seconde étape, nous utilisons un algorithme Metropolis-within-Gibbs couplé à la grouping (ou blocking) technique de Liu (1994) afin de surmonter certaines difficultés d'échantillonnage. Ce choix a des avantages théoriques et computationnels. La méthode développée est appliquée à des jeux de données microarray sur le cancer du sein. Cependant elle a une limite : la matrice de covariance utilisée dans le g-prior doit nécessairement être inversible. Or il y a deux cas pour lesquels cette matrice est singulière : lorsque le nombre de variables sélectionnées dépasse le nombre d'observations, ou lorsque des variables sont combinaisons linéaires d'autres variables. Nous proposons donc une modification de l'a priori de Zellner en y introduisant un paramètre de type ridge, ainsi qu'une manière de choisir les hyper-paramètres associés. L'a priori obtenu est un compromis entre le g-prior classique et l'a priori supposant l'indépendance des coefficients de régression, et se rapproche d'un a priori précédemment proposé par Gupta et Ibrahim (2007).Dans une seconde partie nous développons deux nouvelles méthodes MCMC basées sur des populations de chaînes. Dans le cas de modèles complexes ayant de nombreux paramètres, mais où la vraisemblance des données peut se calculer, l'algorithme Equi-Energy Sampler (EES) introduit par Kou et al. (2006) est apparemment plus efficace que l'algorithme classique du Parallel Tempering (PT) introduit par Geyer (1991). Cependant, il est difficile d'utilisation lorsqu'il est couplé avec un échantillonneur de Gibbs, et nécessite un stockage important de valeurs. Nous proposons un algorithme combinant le PT avec le principe d'échanges entre chaînes ayant des niveaux d'énergie similaires dans le même esprit que l'EES. Cette adaptation appelée Parallel Tempering with Equi-Energy Moves (PTEEM) conserve l'idée originale qui fait la force de l'algorithme EES tout en assurant de bonnes propriétés théoriques et une utilisation facile avec un échantillonneur de Gibbs.Enfin, dans certains cas complexes l'inférence peut être difficile car le calcul de la vraisemblance des données s'avère trop coûteux, voire impossible. De nombreuses méthodes sans vraisemblance ont été développées. Par analogie avec le Parallel Tempering, nous proposons une méthode appelée ABC-Parallel Tempering, basée sur la théorie des MCMC, utilisant une population de chaînes et permettant des échanges entre elles. / This thesis is divided into two main parts. In the first part, we propose a Bayesian variable selection method for probit mixed models. The objective is to select few relevant variables among tens of thousands while taking into account the design of a study, and in particular the fact that several datasets are merged together. The probit mixed model used is considered as part of a larger hierarchical Bayesian model, and the dataset is introduced as a random effect. The proposed method extends a work of Lee et al. (2003). The first step is to specify the model and prior distributions. In particular, we use the g-prior of Zellner (1986) for the fixed regression coefficients. In a second step, we use a Metropolis-within-Gibbs algorithm combined with the grouping (or blocking) technique of Liu (1994). This choice has both theoritical and practical advantages. The method developed is applied to merged microarray datasets of patients with breast cancer. However, this method has a limit: the covariance matrix involved in the g-prior should not be singular. But there are two standard cases in which it is singular: if the number of observations is lower than the number of variables, or if some variables are linear combinations of others. In such situations we propose to modify the g-prior by introducing a ridge parameter, and a simple way to choose the associated hyper-parameters. The prior obtained is a compromise between the conditional independent case of the coefficient regressors and the automatic scaling advantage offered by the g-prior, and can be linked to the work of Gupta and Ibrahim (2007).In the second part, we develop two new population-based MCMC methods. In cases of complex models with several parameters, but whose likelihood can be computed, the Equi-Energy Sampler (EES) of Kou et al. (2006) seems to be more efficient than the Parallel Tempering (PT) algorithm introduced by Geyer (1991). However it is difficult to use in combination with a Gibbs sampler, and it necessitates increased storage. We propose an algorithm combining the PT with the principle of exchange moves between chains with same levels of energy, in the spirit of the EES. This adaptation which we are calling Parallel Tempering with Equi-Energy Move (PTEEM) keeps the original idea of the EES method while ensuring good theoretical properties and a practical use in combination with a Gibbs sampler.Then, in some complex models whose likelihood is analytically or computationally intractable, the inference can be difficult. Several likelihood-free methods (or Approximate Bayesian Computational Methods) have been developed. We propose a new algorithm, the Likelihood Free-Parallel Tempering, based on the MCMC theory and on a population of chains, by using an analogy with the Parallel Tempering algorithm.

In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both complete and partial information. We study partially observable stochastic games with average cost criterion and the state process be-ing discrete time controlled Markov chain. The idea involved in studying this problem is to replace the original unobservable state variable with a suitable completely observable state variable. We establish the existence of the value of the game and also obtain optimal strategies for both players. We also study a continuous time zero-sum stochastic game with complete observation. In this case the state is a pure jump Markov process. We investigate the nite horizon total cost criterion. We characterise the value function via appropriate Isaacs equations. This also yields optimal Markov strategies for both players. In the single player setup we investigate risk-sensitive control of continuous time Markov chains. We consider both nite and in nite horizon problems. For the nite horizon total cost problem and the in nite horizon discounted cost problem we characterise the value function as the unique solution of appropriate Hamilton Jacobi Bellman equations. We also derive optimal Markov controls in both the cases. For the in nite horizon average cost case we shown the existence of an optimal stationary control. we also give a value iteration scheme for computing the optimal control in the case of nite state and action spaces. Further we introduce a new class of stochastic processes which we call stochastic processes with \age-dependent transition rates". We give a rigorous construction of the process. We prove that under certain assunptions the process is Feller. We also compute the limiting probabilities for our process. We then study the controlled version of the above process. In this case we take the risk-neutral cost criterion. We solve the in nite horizon discounted cost problem and the average cost problem for this process. The crucial step in analysing these problems is to prove that the original control problem is equivalent to an appropriate semi-Markov decision problem. Then the value functions and optimal controls are characterised using this equivalence and the theory of semi-Markov decision processes (SMDP). The analysis of nite horizon problems becomes di erent from that of in nite horizon problems because of the fact that in this case the idea of converting into an equivalent SMDP does not seem to work. So we deal with the nite horizon total cost problem by showing that our problem is equivalent to another appropriately de ned discrete time Markov decision problem. This allows us to characterise the value function and to nd an optimal Markov control.