Modeling financial time series is of great importance for being successful within the financial market. Hidden Markov Models is a great way to include the regime shifting nature of financial data. This thesis will focus on getting an in depth knowledge of Hidden Markov Models in general and specifically the parameter estimation of the models. The objective will be to evaluate if and how financial data can be fitted nicely with the model. The subject was requested by Nordea Markets with the purpose of gaining knowledge of HMM’s for an eventual implementation of the theory by their index development group. The research chiefly consists of evaluating the algorithmic behavior of estimating model parameters. HMM’s proved to be a good approach of modeling financial data, since much of the time series had properties that supported a regime shifting approach. The most important factor for an effective algorithm is the number of states, easily explained as the distinguishable clusters of values. The suggested algorithm of continuously modeling financial data is by doing an extensive monthly calculation of starting parameters that are used daily in a less time consuming usage of the EM-algorithm.

Masters of Science / Much work has been done in building systems that can recognise gestures, e.g. as a component of sign language recognition systems. These systems typically use whole gestures as the smallest unit for recognition. Although high recognition rates have been reported, these systems do not scale well and are computationally intensive. The reason why these systems generally scale poorly is that they recognize gestures by building individual models for each separate gesture; as the number of gestures grows, so does the required number of models. Beyond a certain threshold number of gestures to be recognized, this approach becomes infeasible. This work proposes that similarly good recognition rates can be achieved by building models for subcomponents of whole gestures, so-called cheremes. Instead of building models for entire gestures, we build models for cheremes and recognize gestures as sequences of such cheremes. The assumption is that many gestures share cheremes and that the number of cheremes necessary to describe gestures is much smaller than the number of gestures. This small number of cheremes then makes it possible to recognize a large number of gestures with a small number of chereme models. This approach is akin to phoneme-based speech recognition systems where utterances are recognized as phonemes which in turn are combined into words. We attempt to recognise and classify cheremes found in South African Sign Language (SASL). We introduce a method for the automatic discovery of cheremes in dynamic signs. We design, train and use hidden Markov models (HMMs) for chereme recognition. Our results show that this approach is feasible in that it not only scales well, but it also generalizes well. We are able to recognize cheremes in signs that were not used for training HMMs; this generalization ability is a basic necessity for chemere-based gesture recognition. Our approach can thus lay the foundation for building a SASL dynamic gesture recognition system.

Indiana University-Purdue University Indianapolis (IUPUI) / Bayesian networks, one of the most widely used techniques to understand or predict the future by making use of current or previous data, have gained credence over the last decade for their ability to simulate large gene expression datasets to track and predict the reasons for changes in biological systems. In this work, we present a dynamic Bayesian model with gene annotation scores such as the gene characterization index (GCI) and the GenCards inferred functionality score (GIFtS) to understand and assess the prediction performance of the model by incorporating prior knowledge. Time-course breast cancer data including expression data about the genes in the breast cell-lines when treated with doxorubicin is considered for this study. Bayes server software was used for the simulations in a dynamic Bayesian environment with 8 and 19 genes on 12 different data combinations for each category of gene set to predict and understand the future time- course expression profiles when annotation scores are incorporated into the model. The 8-gene set predicted the next time course with r>0.95, and the 19-gene set yielded a value of r>0.8 in 92% cases of the simulation experiments. These results showed that incorporating prior knowledge into the dynamic Bayesian model for simulating the time- course expression data can improve the prediction performance when sufficient apriori parameters are provided.

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Document classification is used to sort and label documents. This gives users quicker access to relevant data. Users that work with large inflow of documents spend time filing and categorizing them to allow for easier procurement. The Automatic Classification and Document Filing (ACDF) system proposed here is designed to allow users working with files or documents to rely on the system to classify and store them with little manual attention. By using a system built on Hidden Markov Models, the documents in a smaller desktop environment are categorized with better results than the traditional Naive Bayes implementation of classification.

This thesis presents an automatic soil texture classification system using hyperspectral soil signals and wavelet-based statistical models. Previous soil texture classification systems are closely related to texture classification methods, which use images for training and testing. Although using image-based algorithms is a straightforward way to conduct soil texture classification, our research shows that it does not provide reliable and consistent results. Rather, we develop a novel system using hyperspectral soil textures, better known as hyperspectral soil signals, which provide rich information and intrinsic properties about soil textures. Hyperspectral soil textures, in their very nature, are nonstationary and time-varying. Therefore, the wavelet transform, which is proven to be successful in such applications, is incorporated. In this study, we incorporate two wavelet-domain statistical models, namely, the maximum likelihood (ML) and the hidden Markov model (HMM) for the classification task. Experimental results show that this method is reliable and robust. It is also more effective and efficient in terms of practical implementation than the traditional image-based methods.

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