Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a cell biology class at Brigham Young University. The mixing proportion was examined to draw conclusions about bimodality. We were successful in fitting the beta mixture to the data, but the methods were only partially successful in detecting bimodality.

No description available.

The quantitative analysis of complex gas mixtures, such as the hydrazines and their air oxidation products, is of paramount importance in closed cycle systems used, for example, in submarines. A laser optoacoustic (photoacoustic) spectrometer which is capable of detecting these species at parts per billion levels has been developed and a system for field use is described. Laser optoacoustic measurements have been made on a range of other species which absorb in the CO2 laser region of 9 - 11.3~m, including many atmospheric pollutants such as the chlorofluorocarbons, perfluorocarbons, and some of the new 'ozone friendly' propellant and refrigerant species. Absorption coefficient data and limits of detection have been established for many gaseous molecules, and a series of optoacoustic cells has been designed, together with a novel method for the generation of gaseous species at low concentrations. A CO2 laser based optoacoustic spectrometer is compared favourably with a range of other current methods used to detect low levels of atmospheric contaminants, and has been shown to be a most suitable technique for the quantitative detection of a wide range of substances at the parts per billion level.

No description available.

Prostate Cancer (PC) is associated with disease- and treatment-related side effects that can compromise quality of life (QoL). Psychosocial interventions designed to improve adjustment and quality of life (QoL) for post-treatment PC patients have been conducted with mixed results. Intervention effects are typically analyzed using either mean difference scores or a single estimate of growth parameters (e.g., intercept and slope factors) across groups. These methods assume homogeneity within groups. Evidence suggests, however, considerable variability both in the experience of disease-specific outcomes and in the long-term adjustment and emotional well-being of men with PC. The present study used growth mixture modeling (GMM) to explore the effects of a cognitive behavioral stress management (CBSM) intervention on emotional well-being among men recently treated for localized PC. This methodology allowed examination of intervention effects across unobserved subgroups characterized by different trajectories of emotional well-being and identified factors associated with intervention efficacy.

This study integrated variable- and child-centered techniques to investigate trajectories of four learning behaviors (initiative, persistence, planning, and problem-solving flexibility) and their influence on Head Start preschoolers' academic school readiness. Variable-centered findings revealed differential, quadratic growth trajectories for each of the four learning behaviors. However, where children began the year (intercept), how much they changed across the year (slope), and how much their rate of change changed across the year (quadratic) differed depending on the learning behavior. Initiative and problem-solving flexibility emerged as significant predictors of end-of-year academic school readiness skills, controlling for persistence and planning. There was no evidence of moderation of the relations between learning behaviors and academic skills by child demographic characteristics. Child-centered results provided a more nuanced description of the development of these four learning behaviors. Analyses suggested there may be subgroups of children with different developmental trajectories for each of the four learning behaviors and that these subgroups have significantly different school readiness skills at the end of the year. These findings help extend our current understanding of learning behaviors and, if replicated, may inform the content and timing of early childhood teaching practices and interventions.

Mixture models are useful in describing a wide variety of random phenomena because of their flexibility in modeling. They have continued to receive increasing attention over the years from both a practical and theoretical point of view. In their applications, estimating the number of mixture components is often the main research objective or the first step toward it. Estimation of the number of mixture components heavily depends on the underlying distribution. As an extension of normal mixture models, we introduce a skew-normal mixture model and adapt the reversible jump Markov chain Monte Carlo algorithm to estimate the number of components with some applications to biological data. The reversible jump algorithm is also applied to the Cox proportional hazard model with frailty. We consider a regression model for the variance components in the proportional hazards frailty model. We propose a Bayesian model averaging procedure with a reversible jump Markov chain Monte Carlo step which selects the model automatically. The resulting regression coefficient estimates ignore the model uncertainty from the frailty distribution. Finally, the proposed model and the estimation procedure are illustrated with simulated example and real data.

Darbe nagrinėjame ėmimo planus, kurių priklausymo imčiai tikimybės yra dviejų komponenčių mišiniai. Pirmoji komponentė yra proporcinga papildoma informacija nusakytam populiacijos elemento dydžiui, o antroji yra vienoda visiems elementams. Ieškome tokių mišinių, kurie minimizuoja įvairių populiacijos sumos įvertinių dispersijas ir parodome kaip, naudojantis papildoma informacija, apytiksliai nustatyti optimalų mišinį. Pateikiame teorinius ir kompiuterinio modeliavimo rezultatus Poisson'o imtims, renkamoms iš populiacijų, kurios yra generuotos naudojant tiesinės regresijos modelį. / We consider sampling designs, where inclusion (to sample) probabilities are mixtures of two components. The first component is proportional to the size of a population unit (described by means of an auxiliary information available). The second component is the same for every unit. We look for mixtures that minimize variances of various estimators of the population total and show how auxiliary information could help to find an approximate location of such mixtures. We report theoretical and simulation results in the case of Poisson samples drawn from populations which are generated by a linear regression model.

Environmental exposure and outcomes assessment is a great challenge to scientists. Increasingly more and more detailed data are becoming available to understand the nature and complexity of the relationships involved. The methodology of mixture models provides a means to understand, quantify and describe features and relation- ships within complex data sets. In this thesis, we focussed on a number of applied problems to characterise complex environmental exposure and outcomes, including: assessing the interaction between environmental exposures as risk factors for health outcomes; identifying di®ering environmental outcomes across a region; and estab- lishing patterns in the size and concentration of aerosol particles over time. Mixture model approaches to address these problems are developed and examined for their suitability in these contexts.

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme. This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme.