Random heterogeneous, scale-dependent structures can be observed from many image sources, especially from remote sensing and scientific imaging. Examples include slices of porous media data showing pores of various sizes, and a remote sensing image including small and large sea-ice blocks. Meanwhile, rather than the images of phenomena themselves, there are many image processing and analysis problems requiring to deal with \emph{discrete-state} fields according to a labeled underlying property, such as mineral porosity extracted from microscope images, or an ice type map estimated from a sea-ice image. In many cases, if discrete-state problems are associated with heterogeneous, scale-dependent spatial structures, we will have to deal with complex discrete state fields. Although scale-dependent image modeling methods are common for continuous-state problems, models for discrete-state cases have not been well studied in the literature. Therefore, a fundamental difficulty will arise which is how to represent such complex discrete-state fields. Considering the success of hidden field methods in representing heterogenous behaviours and the capability of hierarchical field methods in modeling scale-dependent spatial features, we propose a Hidden Hierarchical Markov Field (HHMF) approach, which combines the idea of hierarchical fields with hidden fields, for dealing with the discrete field modeling challenge. However, to define a general HHMF modeling structure to cover all possible situations is difficult. In this research, we use two image application problems to describe the proposed modeling methods: one for scientific image (porous media image) reconstruction and the other for remote-sensing image synthesis. For modeling discrete-state fields with a spatially separable complex behaviour, such as porous media images with nonoverlapped heterogeneous pores, we propose a Parallel HHMF model, which can decomposes a complex behaviour into a set of separated, simple behaviours over scale, and then represents each of these with a hierarchical field. Alternatively, discrete fields with a highly heterogeneous behaviour, such as a sea-ice image with multiple types of ice at various scales, which are not spatially separable but arranged more as a partition tree, leads to the proposed Tree-Structured HHMF model. According to the proposed approach, a complex, multi-label field can be repeatedly partitioned into a set of binary/ternary fields, each of which can be further handled by a hierarchical field.

Hidden Markov models have become a popular tool for modeling long-term investment guarantees. Many different variations of hidden Markov models have been proposed over the past decades for modeling indexes such as the S&P 500, and they capture the tail risk inherent in the market to varying degrees. However, goodness-of-fit testing, such as residual-based testing, for hidden Markov models is a relatively undeveloped area of research. This work focuses on hidden Markov model assessment, and develops a stochastic approach to deriving a residual set that is ideal for standard residual tests. This result allows hidden-state models to be tested for goodness-of-fit with the well developed testing strategies for single-state models. This work also focuses on parameter uncertainty for the popular long-term equity hidden Markov models. There is a special focus on underlying states that represent lower returns and higher volatility in the market, as these states can have the largest impact on investment guarantee valuation. A Bayesian approach for the hidden Markov models is applied to address the issue of parameter uncertainty and the impact it can have on investment guarantee models. Also in this thesis, the areas of portfolio optimization and portfolio replication under a hidden Markov model setting are further developed. Different strategies for optimization and portfolio hedging under hidden Markov models are presented and compared using real world data. The impact of parameter uncertainty, particularly with model parameters that are connected with higher market volatility, is once again a focus, and the effects of not taking parameter uncertainty into account when optimizing or hedging in a hidden Markov are demonstrated.

<p>Large-scale, in vitro vaccine screening is an expensive and slow process, while rational vaccine design is faster and cheaper. As opposed to the emperical ways to design vaccines in biology laboratories, rational vaccine design models the structure of vaccines with computational approaches. Building an effective predictive computer model requires extensive knowledge of the process or phenomenon being modelled. Given current knowledge about the steps involved in immune system responses, computer models are currently focused on one or two of the most important and best known steps; for example: presentation of antigens by major histo-compatibility complex (MHC) molecules. In this step, the MHC molecule selectively binds to some peptides derived from antigens and then presents them to the T-cell. One current focus in rational vaccine design is prediction of peptides that can be bound by MHC.<p>Theoretically, predicting which peptides bind to a particular MHC molecule involves discovering patterns in known MHC-binding peptides and then searching for peptides which conform to these patterns in some new antigenic protein sequences. According to some previous work, Hidden Markov models (HMMs), a machine learning technique, is one of the most effective approaches for this task. Unfortunately, for computer models like HMMs, the number of the parameters to be determined is larger than the number which can be estimated from available training data.<p>Thus, heuristic approaches have to be developed to determine the parameters. In this research, two heuristic approaches are proposed. The rst initializes the HMM transition and emission probability matrices by assigning biological meanings to the states. The second approach tailors the structure of a fully connected HMM (fcHMM) to increase specicity. The effectiveness of these two approaches is tested on two human leukocyte antigens(HLA) alleles, HLA-A*0201 and HLAB* 3501. The results indicate that these approaches can improve predictive accuracy. Further, the HMM implementation incorporating the above heuristics can outperform a popular prole HMM (pHMM) program, HMMER, in terms of predictive accuracy.

Multivariate count data are found in a variety of fields. For modeling such data, one may consider the multivariate Poisson distribution. Overdispersion is a problem when modeling the data with the multivariate Poisson distribution. Therefore, in this thesis we propose a new multivariate Poisson hidden Markov model based on the extension of independent multivariate Poisson finite mixture models, as a solution to this problem. This model, which can take into account the spatial nature of weed counts, is applied to weed species counts in an agricultural field. The distribution of counts depends on the underlying sequence of states, which are unobserved or hidden. These hidden states represent the regions where weed counts are relatively homogeneous. Analysis of these data involves the estimation of the number of hidden states, Poisson means and covariances. Parameter estimation is done using a modified EM algorithm for maximum likelihood estimation. <p>We extend the univariate Markov-dependent Poisson finite mixture model to the multivariate Poisson case (bivariate and trivariate) to model counts of two or three species. Also, we contribute to the hidden Markov model research area by developing Splus/R codes for the analysis of the multivariate Poisson hidden Markov model. Splus/R codes are written for the estimation of multivariate Poisson hidden Markov model using the EM algorithm and the forward-backward procedure and the bootstrap estimation of standard errors. The estimated parameters are used to calculate the goodness of fit measures of the models.<p>Results suggest that the multivariate Poisson hidden Markov model, with five states and an independent covariance structure, gives a reasonable fit to this dataset. Since this model deals with overdispersion and spatial information, it will help to get an insight about weed distribution for herbicide applications. This model may lead researchers to find other factors such as soil moisture, fertilizer level, etc., to determine the states, which govern the distribution of the weed counts.

This thesis investigates the design and implementation strategies for a Spanish speech recognition system. It utilizes the speech features of the 242 common Spanish mono-syllables as the major training and recognition methodology. A training database of twelve utterances per mono-syllable is established by applying Spanish pronunciation rules. These twelve utterances are collected through reading six rounds of the same mono-syllable with two different tones. The first pronounced pattern has high pitch of tone one, while the second one has falling pitch of tone four. Mel-frequency cepstral coefficients, linear predictive cepstral coefficients, and hidden Markov model are used as the two feature models and the recognition model respectively. Under the AMD Sempron Processor 2800+ with 1.6GHz clock rate personal computer and Ubuntu 9.04 operating system environment, a correct phrase recognition rate of 86% can be reached for a 4217 Spanish phrase database. The average computation time for each phrase is about 1.5 seconds.

This thesis investigates the design and implementation strategies for a French speech recognition system. It utilizes the speech features of the 425 common French mono-syllables as the major training and recognition methodology. A training database is established by reading each mono-syllable 12 times in 6 rounds. Every mono-syllable is consecutively read twice with different tones. The first pronounced pattern has high pitch of tone 1,while the second one has falling pitch of tone 4. Mel-frequency cepstrum coefficients, linear predictive cepstrum coefficients, and hidden Markov model are used as the two feature models and the recognition model respectively. Under the AMD Athlon xp 2800+ with clock rate 2.2GHz personal computer and Ubuntu 9.04 operating system environment, a correct phrase recognition rate of 86% can be reached for a 3850 French phrase database. The average computation time for each phrase is about 1.5 seconds.

This thesis investigates the design and implementation strategies for a German speech recognition system. It utilizes the speech features of the 434 common German mono-syllables as the major training and recognition methodology. A training database is established by reading each mono-syllable 12 times in 6 rounds. Every mono-syllable is consecutively read twice with different tones. The first pronounced pattern has high pitch of tone 1, while the second one has falling pitch of tone 4. Mel-frequency cepstral coefficients, linear predictive cepstral coefficients, and hidden Markov model are used as the two feature models and the recognition model respectively. Under the AMD Athlon X2-240 with 2.8 GHz clock rate personal computer and Ubuntu 9.04 operating system environment, a correct phrase recognition rate of 84% can be reached for a 3900 German phrase database. The average computation time for each phrase is within 1 second.

This thesis investigates the design and implementation strategies for a Korean speech recognition system. It utilizes the speech features of the common Korean mono-syllables as the major training and recognition methodology. A training database of 10 utterances per mono-syllable is established by applying Korean pronunciation rules. These 10 utterances are collected through reading 5 rounds of the same mono-syllables twice with different tones. The first pronounced pattern has high pitch of tone 1,while the second one has falling pitch of tone 4.Mel-frequency cepstral coefficients, linear predictive cepstrum coefficients, and hidden Markov model are used as the two feature models and the recognition model respectively. Under the Pentium 2.4 GHz personal computer and Ubuntu 9.04 operating system environment, a correct phrase recognition rate of 92.25% can be reached for a 4865 Korean phrase database. The average computation time for each phrase is about 1.5 seconds.

IBM, a well-known computer giant, and Nuance, a renowned speech technology firm, have been offering numerous speech recognition applications in the recent years. The connections between these two companies and the automobile, communication, and other eight dominating industries, including banking, electronics, energy/utilities, medical/life science, insurance, media/entertainment, retail travel and transportation, are vastly expanded and flourished. Maturity of these speech technologies drives our lifestyle to a cozy level that we cannot imagine before. In April, 2011, the world class manufacturer Foxconn decided to invest 12 billion US dollars to build iPhone/iPad factories in Brazil, the largest Portuguese speaking country in the world. It is our objective to build a language system that can help us to learn Portuguese, to savor the beauty of their culture, and to widen our vision of travel and living. This thesis investigates the design and implementation strategies for a Portuguese speech recognition system. It utilizes the speech features of the 303 common Portuguese mono-syllables as the major training and recognition methodology. A training database of 10 utterances per mono-syllable is established by applying Portuguese pronunciation rules. These 10 utterances are collected through reading 5 rounds of the same mono-syllables twice with different tones. The first pronounced pattern has high pitch of tone 1, while the second one has falling pitch of tone 4. Mel-frequency cepstral coefficients, linear predicted cepstral coefficients, and hidden Markov model are used as the two syllable feature models and the recognition model respectively. Under the AMD 2.2 GHz Athlon XP 2800+ personal computer and Ubuntu 9.04 operating system environment, correct phrase recognition rates of 87.26% can be reached using phonotactical rules for a 3,900 vocabulary Portuguese phrase database. The average computation time for the Portuguese phrase system is less than 1.5 seconds, and the training time for the systems is about two hours.

Language plays an important role for understanding people, their history, culture and even technology. Many countries of the world have developed the technology of the outer space recently, and Russian is the top of the world. In 1998 Russia further launched Zarya, the first International Space Station (ISS) Module, to the outer space, and was deeply involved in the development of the ISS with the U.S.. Since the end of the World War Two, Russia has been one of the five Permanent Members in the United Nations. And then, she became one of the G8 members, an economical forum of eight industrially advanced nations. Because these informations, it is our objective to build a language system that can help us to learn Russian, to taste the beauty of her culture, and to widen our vision of technologies. This thesis investigates the design and implementation strategies for a Russian speech recognition system. It utilizes the speech features of the 514 common Russian mono-syllables as the major training and recognition methodology. The mono-syllable is established by applying Russian pronunciation rules. These 12 utterances are collected through reading 6 rounds of the same mono-syllables twice with different tones. The first pronounced pattern has high pitch of tone 1, while the second one has falling pitch of tone 4. Mel-frequency cepstral coefficients, linear predicted cepstral coefficients, and hidden Markov model are used as the two syllable feature models and the recognition model respectively. Under the AMD 2.2 GHz Athlon XP 2800+ personal computer and Ubuntu 9.04 operating system environment, correct phrase recognition rates of 86.90% and 94.83% can be reached using phonotactical rules for a 3,900 vocabulary Russian phrase database for TORFL (Test of Russian as a Foreign Language) and a 600 person name database for Russian. The average computation time for each system is less than 1.5 seconds, and the training time for the systems is about three hours.