Many firms are challenged to make inventory decisions with limited data, and high customer service level requirements. This thesis focuses on heuristic solutions for inventory management problems in data-scarce environments, employing rigorous mathematical frameworks and taking advantage of the information that is available in practice but often ignored in literature. We define a class of inventory models and solutions with demonstrable value in helping firms solve these challenges.

Estudos comportamentais têm sido conduzidos, há séculos, por cientistas e filósofos, abordando assuntos tais como trajetórias de estrelas e planetas, organizações da sociedade, evolução dos seres vivos, comportamento e linguagem humana. Com o advento da computação, grandes quantidades de informação tornaram-se disponíveis, as quais geram novos desafios a fim de explorar e compreender variações comportamentais de interação com esses sistemas. Motivado por esses desafios e pela disponibilidade de informações, esta dissertação de mestrado propõe uma metodologia com objetivo de classificar, detectar e identificar padrões de comportamento. A fim de validar essa metodologia, modelou-se conhecimentos embutidos em informações relativas a interações de usuários durante a grafia digital de assinaturas (tais informações foram obtidas de uma base de dados do campeonato SVC2004 -- First International Signature Verification Competition). Os modelos de conhecimento gerados foram, posteriormente, empregados em experimentos visando o reconhecimento de assinaturas. Resultados obtidos foram comparados a outras abordagens propostas na literatura / Throughout the centuries, behavioral studies have been conducted by scientists and philosophers, approaching subjects such as stars and planet trajectories, social organizations, living beings, human behavior and language. With the advent of computer science, large amounts of information have been made available, which brings out new challenges in the interactive behavior context. Such challenges have motivated this master thesis which proposes a methodology to classify, detect and identify behavioral patterns. A digital signature verification database, obtained from the First International Signature Verification Competition (SVC2004), was used to validate the proposed methodology. Knowledge models were obtained and, afterwards, employed in signature verification experiments. Results were compared to other approaches from the literature

O labirinto em cruz elevado é muito usado em estudos relacionados à ansiedade em ratos. As medidas tradicionalmente usadas são o número de entradas e o tempo passado nos braços abertos. Trabalhos recentes analisam a movimentação no interior dos braços, mas não propõem um índice que resuma as análises feitas. Esta tese sintetiza as informações de um destes trabalhos em índices. Um dos índices propostos usa os tempos médios de primeira visita a cada posição do labirinto e o outro se baseia na distribuição estacionária de probabilidade, o primeiro é capaz de diferenciar grupos de ratos submetidos a diferentes drogas ansiolíticas. Além disso, a tese propõe um modelo de processo Markoviano que incorpora informações desconsideradas no modelo anterior. A comparação entre os modelos revelou valores super ou subestimados no primeiro. Por fim, esta tese propõe um modelo de cadeias de Markov considerando como estados o seguinte conjunto de comportamentos: \"rearing\", \"stretching\", \"dipping\", \"freezing\" e \"grooming\". Tal abordagem inédita, apesar de simplificar exageradamente o modelo, foi capaz de reproduzir várias características conhecidas da exploração. / The elevated plus maze is widely used in studies related to anxiety in rats. The most widely used measures are the amount of entries and time spent on open arms. Recent studies analyze the movement inside the arms, but do not propose an index that summarizes the analyzes. This thesis summarizes by indices the information in one of these studies. An index uses the first visit average time to each position of the maze and another is based on the stationary probability distribution, the first one are able to differentiate groups of rats submitted to different anxiolytic drugs. These thesis also proposes a Markov process model that incorporates more information than the other model. The comparison between the models showed over- or underestimated values in the first. Finally, this thesis proposes a Markov chains model considering the following behaviors as states: rearing, stretching, dipping, freezing and grooming. This new approach, though oversimplify the model was able to reproduce several known features of exploitation.

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance vis--vis the more common maximum likelihood-based model selection on both simulated and real market data. All five MCMC methods proved feasible in both cases, although differing in their computational demands. Results on simulated data show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favour of the true model than maximum likelihood. Results on market data show the feasibility of all model selection methods, mainly because the distributions appear to be decisively non-Gaussian. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Estudos comportamentais têm sido conduzidos, há séculos, por cientistas e filósofos, abordando assuntos tais como trajetórias de estrelas e planetas, organizações da sociedade, evolução dos seres vivos, comportamento e linguagem humana. Com o advento da computação, grandes quantidades de informação tornaram-se disponíveis, as quais geram novos desafios a fim de explorar e compreender variações comportamentais de interação com esses sistemas. Motivado por esses desafios e pela disponibilidade de informações, esta dissertação de mestrado propõe uma metodologia com objetivo de classificar, detectar e identificar padrões de comportamento. A fim de validar essa metodologia, modelou-se conhecimentos embutidos em informações relativas a interações de usuários durante a grafia digital de assinaturas (tais informações foram obtidas de uma base de dados do campeonato SVC2004 -- First International Signature Verification Competition). Os modelos de conhecimento gerados foram, posteriormente, empregados em experimentos visando o reconhecimento de assinaturas. Resultados obtidos foram comparados a outras abordagens propostas na literatura / Throughout the centuries, behavioral studies have been conducted by scientists and philosophers, approaching subjects such as stars and planet trajectories, social organizations, living beings, human behavior and language. With the advent of computer science, large amounts of information have been made available, which brings out new challenges in the interactive behavior context. Such challenges have motivated this master thesis which proposes a methodology to classify, detect and identify behavioral patterns. A digital signature verification database, obtained from the First International Signature Verification Competition (SVC2004), was used to validate the proposed methodology. Knowledge models were obtained and, afterwards, employed in signature verification experiments. Results were compared to other approaches from the literature

The No-U-Turn Sampler (NUTS) is a relatively new Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior that common MCMC algorithms such as Gibbs sampling or Metropolis Hastings usually exhibit. Given the fact that NUTS can efficiently explore the entire space of the target distribution, the sampler converges to high-dimensional target distributions more quickly than other MCMC algorithms and is hence less computational expensive. The focus of this study is on applying NUTS to one of the complex IRT models, specifically the two-parameter mixture IRT (Mix2PL) model, and further to examine its performance in estimating model parameters when sample size, test length, and number of latent classes are manipulated. The results indicate that overall, NUTS performs well in recovering model parameters. However, the recovery of the class membership of individual persons is not satisfactory for the three-class conditions. Also, the results indicate that WAIC performs better than LOO in recovering the number of latent classes, in terms of the proportion of the time the correct model was selected as the best fitting model. However, when the effective number of parameters was also considered in selecting the best fitting model, both fully Bayesian fit indices perform equally well. In addition, the results suggest that when multiple latent classes exist, using either fully Bayesian fit indices (WAIC or LOO) would not select the conventional IRT model. On the other hand, when all examinees came from a single unified population, fitting MixIRT models using NUTS causes problems in convergence.

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

Conventional probabilistic models for phylogenetic inference assume that an evolutionary tree,andasinglesetofbranchlengthsandstochasticprocessofDNA evolutionare sufficient to characterise the generating process across an entire DNA alignment. Unfortunately such a simplistic, homogeneous formulation may be a poor description of reality when the data arise from heterogeneous processes. A well-known example is when sites evolve at heterogeneous rates. This thesis is a contribution to the modelling and understanding of heterogeneityin phylogenetic data. Weproposea methodfor the classificationof DNA sites based on Bayesian mixture modelling. Our method not only accounts for heterogeneous data but also identifies the underlying classes and enables their interpretation. We also introduce novel MCMC methodology with the same, or greater, estimation performance than existing algorithms but with lower computational cost. We find that our mixture model can successfully detect evolutionary heterogeneity and demonstrate its direct relevance by applying it to real DNA data. One of these applications is the analysis of sixteen strains of one of the bacterial species that cause Lyme disease. Results from that analysis have helped understanding the evolutionary paths of these bacterial strains and, therefore, the dynamics of the spread of Lyme disease. Our method is discussed in the context of DNA but it may be extendedto othertypesof molecular data. Moreover,the classification scheme thatwe propose is evidence of the breadth of application of mixture modelling and a step forwards in the search for more realistic models of theprocesses that underlie phylogenetic data.

The analysis of sequential data is important in business, science, and engineering, for tasks such as signal processing, user behavior mining, and commercial transactions analysis. In this dissertation, we build upon the Collective Dynamical Modeling and Clustering (CDMC) framework for discrete time series modeling, by making contributions to clustering initialization, dynamical modeling, and scaling. We first propose a modified Dynamic Time Warping (DTW) approach for clustering initialization within CDMC. The proposed approach provides DTW metrics that penalize deviations of the warping path from the path of constant slope. This reduces over-warping, while retaining the efficiency advantages of global constraint approaches, and without relying on domain dependent constraints. Second, we investigate the use of semi-Markov chains as dynamical models of temporal sequences in which state changes occur infrequently. Semi-Markov chains allow explicitly specifying the distribution of state visit durations. This makes them superior to traditional Markov chains, which implicitly assume an exponential state duration distribution. Third, we consider convergence properties of the CDMC framework. We establish convergence by viewing CDMC from an Expectation Maximization (EM) perspective. We investigate the effect on the time to convergence of our efficient DTW-based initialization technique and selected dynamical models. We also explore the convergence implications of various stopping criteria. Fourth, we consider scaling up CDMC to process big data, using Storm, an open source distributed real-time computation system that supports batch and distributed data processing. We performed experimental evaluation on human sleep data and on user web navigation data. Our results demonstrate the superiority of the strategies introduced in this dissertation over state-of-the-art techniques in terms of modeling quality and efficiency.

The analysis of big data is of great interest today, and this comes with challenges of improving precision and efficiency in estimation and prediction. We study binary data with covariates from numerous small areas, where direct estimation is not reliable, and there is a need to borrow strength from the ensemble. This is generally done using Bayesian logistic regression, but because there are numerous small areas, the exact computation for the logistic regression model becomes challenging. Therefore, we develop an integrated multivariate normal approximation (IMNA) method for binary data with covariates within the Bayesian paradigm, and this procedure is assisted by the empirical logistic transform. Our main goal is to provide the theory of IMNA and to show that it is many times faster than the exact logistic regression method with almost the same accuracy. We apply the IMNA method to the health status binary data (excellent health or otherwise) from the Nepal Living Standards Survey with more than 60,000 households (small areas). We estimate the proportion of Nepalese in excellent health condition for each household. For these data IMNA gives estimates of the household proportions as precise as those from the logistic regression model and it is more than fifty times faster (20 seconds versus 1,066 seconds), and clearly this gain is transferable to bigger data problems.