Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.

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.

Current physiotherapy practice relies on visual observation of the patient for diagnosis and assessment. The assessment process can potentially be automated to improve accuracy and reliability. This thesis proposes a method to recover patient joint angles and automatically extract movement profiles utilizing small and lightweight body-worn sensors. Joint angles are estimated from sensor measurements via the extended Kalman filter (EKF). Constant-acceleration kinematics is employed as the state evolution model. The forward kinematics of the body is utilized as the measurement model. The state and measurement models are used to estimate the position, velocity and acceleration of each joint, updated based on the sensor inputs from inertial measurement units (IMUs). Additional joint limit constraints are imposed to reduce drift, and an automated approach is developed for estimating and adapting the process noise during on-line estimation. Once joint angles are determined, the exercise data is segmented to identify each of the repetitions. This process of identifying when a particular repetition begins and ends allows the physiotherapist to obtain useful metrics such as the number of repetitions performed, or the time required to complete each repetition. A feature-guided hidden Markov model (HMM) based algorithm is developed for performing the segmentation. In a sequence of unlabelled data, motion segment candidates are found by scanning the data for velocity-based features, such as velocity peaks and zero crossings, which match the pre-determined motion templates. These segment potentials are passed into the HMM for template matching. This two-tier approach combines the speed of a velocity feature based approach, which only requires the data to be differentiated, with the accuracy of the more computationally-heavy HMM, allowing for fast and accurate segmentation. The proposed algorithms were verified experimentally on a dataset consisting of 20 healthy subjects performing rehabilitation exercises. The movement data was collected by IMUs strapped onto the hip, thigh and calf. The joint angle estimation system achieves an overall average RMS error of 4.27 cm, when compared against motion capture data. The segmentation algorithm reports 78% accuracy when the template training data comes from the same participant, and 74% for a generic template.

Longitudinal studies, where data on study subjects are collected over time, is increasingly involving multivariate longitudinal responses. Frequently, the heterogeneity observed in a multivariate longitudinal response can be attributed to underlying unobserved disease states in addition to any between-subject differences. We propose modeling such disease states using a hidden Markov model (HMM) approach and expand upon previous work, which incorporated random effects into HMMs for the analysis of univariate longitudinal data, to the setting of a multivariate longitudinal response. Multivariate longitudinal data are modeled jointly using separate but correlated random effects between longitudinal responses of mixed data types in addition to a shared underlying hidden process. We use a computationally efficient Bayesian approach via Markov chain Monte Carlo (MCMC) to fit such models. We apply this methodology to bivariate longitudinal response data from a smoking cessation clinical trial. Under these models, we examine how to incorporate a treatment effect on the disease states, as well as develop methods to classify observations by disease state and to attempt to understand patient dropout. Simulation studies were performed to evaluate the properties of such models and their applications under a variety of realistic situations.

This qualitative exploratory case study focused on understanding how democracy and human rights education is carried out in a public elementary school in Turkey. A preliminary research was done in the USA in order to provide insight and experience into the study. An elementary school was chosen as a single case in Ankara. The study examined the perceptions of the school community (teachers, students, administrator and parents) related to democracy and human rights education through interviews. The participation to the study was completely based on voluntary action. Six teachers, 38 students, 16 parents and an administrator were interviewed. Observations and document analyses also enabled the researcher to find out the current instructional process concerning democracy and human rights education in different grade levels at elementary education. Content analysis was used to analyze the data. Research results revealed that democracy is not only a goal to be reached, and not just a form of government but also a concept experienced in all stages of schools. The major finding of the study was that there is a gap between what the school teaches as theory and the reality experienced in school and at home. All participants agreed that democracy and human rights education should start at early grades, preferably in kindergarten through establishing authentic learning environments where a variety of instructional methods, techniques, materials, textbooks and technology are employed. Besides, the school community indicated the importance of character education, school culture and values that are reflected through the hidden curriculum in schools for effective democracy and human rights education.

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The thesis deals with how technology as a school subject is presented to the pupils in the Swedish compulsory school at junior high school level. The main focus is on how teachers work with the subject matter in teaching, which is on the level of the enacted curriculum. The official documents established by the national school authorities, the intended curriculum, and the hidden curriculum are both of special interest in the study. The hidden curriculum refers to possible, but not intended consequences of the enacted curriculum for pupils’ understanding of technology as a school subject.            The empirical analysis of the study is based on a narrative analysis on the one hand and the variation theory on the other. The empirical data collection consists of data from: (a) interviews with five teachers and (b) a series of classroom observations, covering an entire section of each teacher’s course of the subject matter.           The data from the interviews with these teachers indicated that they understood the concept of technology as human made artefacts aiming to satisfy practical needs. When it came to the understanding of technology as a school subject the teachers differed between understanding the aim of the subject as to: (1) practice craftsmanship, (2) prepare the pupils for future careers as engineers, (3) illustrate science, (4) strengthen girls’ technical self-confidence and (5) get the pupils interested in technology in order to become inventors in the future. The data from the classroom observations indicated that the teaching presented in technology gave the pupils the opportunity to develop three specific capabilities: (1) evaluate and test functionality, (2) be precise and accurate and (3) construct, build and mount. The three capabilities were possible to develop when accomplishing tasks of practical character. Results also indicated that technology as a school subject was taught in different ways depending on the teachers’ educational background, the physical learning environment and the size of the school class. Variation theory was applied as a tool in the analysis of the data from the classroom observations, i.e. the teachers’ ways of working with the subject matter. The analysis indicated that the most frequently used pattern of variation was ‘contrast’.  Through the contrast-variation the teachers managed to contrast better or worse alternatives of constructing and using artefacts. It can be argued that this pattern of variation, ‘contrast’, is the proper pattern when pupils are working with limited or expensive material.           The overall conclusion of the study is that teachers’ interpretations of current intended curriculum and their choices of subject matter and teaching methods affect which abilities the pupils are offered to develop in technology as a school subject. Based on the results of the study it can be argued that the education and the teaching of technology lacks realism and the result is that technology as a school subject may be experienced by pupils as not very important. It is obvious that the school subject technology, as well as teaching in technology, in the Swedish compulsory school, demands more attention from the national school authorities, in order to develop the pupils’ understanding that technology as a subject is related to the future development of society and social welfare.

In this thesis, methods for achieving finer scale multi-spectral classification through the use of super resolution (SR) techniques are investigated. A new super resolution algorithm Maximum a Posteriori based on the universal hidden Markov tree model (MAP-uHMT) is developed which can be applied successfully to super-resolve each multi-spectral channel before classification by standard methods. It is believed that this is the first time that a true super resolution algorithm has been applied to multi-spectral classification, and results are shown to be excellent. Image registration is an important step for SR in which misalignment can be measured for each of many low resolution images; therefore, a new and computationally efficient image registration is developed for this particular application. This improved elastic image registration method can deal with a global affine warping and local shift translations based on coarse to fine pyramid levels. The experimental results show that it can provide good registration accuracy in less computational time than comparable methods. Maximum a posteriori (MAP) is adopted to deal with the ill-conditioned problem of super resolution, wherein a prior is constructed based on the universal hidden Markov tree (uHMT) model in the wavelet domain. In order to test this prior for MAP estimation, it is first tested in the simpler and typically ill-conditioned problem of image denoising. Experimental results illustrate that this new image denoising method achieves good performance for the test images. The new prior is then extended to SR. By combining with the new elastic image registration algorithm, MAP-uHMT can super resolve both some natural video frames and remote sensing images. Test results with both synthetic data and real data show that this method achieves super resolution both visually and quantitatively. In order to show that MAPuHMT is also applicable more widely, it is tested on a sequence of long-range surveillance images captured under conditions of atmospheric turbulence distortion. The results suggest that super resolution may have been achieved in this application also.

Child survivors of the Holocaust have only recently been recognized as a distinguishable group of individuals who survived the war with a different experience to the older survivors. This thesis focuses on a specific group of child survivors, those who survived by going into hiding. In hiding, some remained "visible" by hiding within convents, orphanages or with Christian families. Others were physically hidden and had to disappear from sight. Most children often combined these two experiences in their hiding. / The intent of this study was to explore the experience of these hidden children using Giorgi’s empirical phenomenological methodology and to gain a richer understanding of the nature of this experience. Phenomenological analyses of the recorded and transcribed interviews of 11 child survivors were conducted and organized into meaning units which subsequently yielded situated structures from which the general structures evolved. / These analyses revealed that the defining moment of being hidden for these children was the suppression of their identities as Jews. By being hidden, they had to deny the essence of their core selves, including their names, family details and connections to others in an effort to conceal their Jewishness. Other structures to emerge as part of hiding were the pervading fear which enveloped their entire experience in hiding and the sense of suspended normality during this period, which sometimes extended over a period of years. A "cut-offness" and personality constriction seemed to be present throughout the descriptions of these children and appears to have developed as a method of coping with the trauma of their childhood. Overlaying all of this were general insecurities about the capriciousness of the war and the contextual specifics of their actual hiding places to which each child had to adjust. Connections/relationships to another person seemed to be highly significant in the dynamics of the everyday during the experience of hiding and often shaped some of the psychological and emotional experiences of hiddenness.