When categorical data are misplaced into the wrong category, we say the data is affected by misclassification. This is common for data collection. It is well-known that naive estimators of category probabilities and coefficients for regression that ignore misclassification can be biased. In this dissertation, we develop methods to provide improved estimators and confidence intervals for a proportion when only a misclassified proxy is observed, and provide improved estimators and confidence intervals for regression coefficients when only misclassified covariates are observed. Following the introduction and literature review, we develop two estimators for a proportion , one which reduces the bias, and one with smaller mean square error. Then we will give two methods to find a confidence interval for a proportion, one using optimization techniques, and the other one using Fieller's method. After that, we will focus on developing methods to find corrected estimators for coefficients of regression with misclassified covariates, with or without perfectly measured covariates, and with a known estimated misclassification/reclassification model. These correction methods use the score function approach, regression calibration and a mixture model. We also use Fieller's method to find a confidence interval for the slope of simple regression with misclassified binary covariates. Finally, we use simulation to demonstrate the performance of our proposed methods.

With the growth of computer power, Digital Image Processing plays a more and more important role in the modern world, including the field of industry, medical, communications, spaceflight technology etc. As a sub-field, Interactive Image Processing emphasizes particularly on the communications between machine and human. The basic flowchart is definition of object, analysis and training phase, recognition and feedback. Generally speaking, the core issue is how we define the interesting object and track them more accurately in order to complete the interaction process successfully. This thesis proposes a novel dynamic simulation scheme for interactive image processing. The work consists of two main parts: Hand Motion Detection and Hand Gesture recognition. Within a hand motion detection processing, movement of hand will be identified and extracted. In a specific detection period, the current image is compared with the previous image in order to generate the difference between them. If the generated difference exceeds predefined threshold alarm, a typical hand motion movement is detected. Furthermore, in some particular situations, changes of hand gesture are also desired to be detected and classified. This task requires features extraction and feature comparison among each type of gestures. The essentials of hand gesture are including some low level features such as color, shape etc. Another important feature is orientation histogram. Each type of hand gestures has its particular representation in the domain of orientation histogram. Because Gaussian Mixture Model has great advantages to represent the object with essential feature elements and the Expectation-Maximization is the efficient procedure to compute the maximum likelihood between testing images and predefined standard sample of each different gesture, the comparability between testing image and samples of each type of gestures will be estimated by Expectation-Maximization algorithm in Gaussian Mixture Model. The performance of this approach in experiments shows the proposed method works well and accurately.

Two very different classes of theoretical models have been proposed to explain visual perception. One class of models assume that there is a point at which we become consciously aware of a stimulus, known as a threshold. This threshold is the foundation of discrete process models all of which describe an all-or-none transition between the mental state of perceiving a stimulus and the state of not perceiving a stimulus. In contrast, the other class of models assume that mental states change continuously. These continuous models are founded in signal detection theory and the more contemporary models in Bayesian inference frameworks. The continuous model is the more widely accepted model of perception, and as such discrete process models were mostly discarded. Nonetheless, there has been a renewed debate on continuous versus discrete perception, and recent work has renewed the idea that perception can be all-or-none. In this dissertation, we developed an experimental platform and modeling framework to test whether visual perception exhibits measurable characteristics consistent with discrete perception. The results of this study revealed a selective influence of stimulus type on the way that a visual stimulus is processed. Moreover this selective influence implied perception can either be discrete or continuous depending on the underlying perceptual processing. These qualitative differences in the way perception occurs even for highly similar stimuli such as motion or orientation have crucial implications for models of perception, as well as our understanding of neurophysiology and conscious perception.

This dissertation develops new approaches for hyperspectral image visualization. Double and multiple layers are proposed to effectively convey the abundant information contained in the original high-dimensional data for practical decision-making support. The contributions of this dissertation are as follows. 1.Development of new visualization algorithms for hyperspectral imagery. Double-layer technique can display mixed pixel composition and global material distribution simultaneously. The pie-chart layer, taking advantage of the properties of non-negativity and sum-to-one abundances from linear mixture analysis of hyperspectral pixels, can be fully integrated with the background layer. Such a synergy enhances the presentation at both macro and micro scales. 2.Design of an effective visual exploration tool. The developed visualization techniques are implemented in a visualization system, which can automatically preprocess and visualize hyperspectral imagery. The interactive tool with a userriendly interface will enable viewers to display an image with any desired level of details. 3.Design of effective user studies to validate and improve visualization methods. The double-layer technique is evaluated by well designed user studies. The traditional approaches, including gray-scale side-by-side classification maps, color hard classification maps, and color soft classification maps, are compared with the proposed double-layer technique. The results of the user studies indicate that the double-layer algorithm provides the best performance in displaying mixed pixel composition in several aspects and that it has the competitive capability of displaying the global material distribution. Based on these results, a multi-layer algorithm is proposed to improve global information display.

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Growth mixture models (GMMs) are used to model intra-individual change and inter-individual differences in change and to detect underlying group structure in longitudinal studies. Regularly, these models are fitted under the assumption of normality, an assumption that is frequently invalid. To this end, this thesis focuses on the development of novel non-elliptical growth mixture models to better fit real data. Two non-elliptical growth mixture models, via the multivariate skew-t distribution and the generalized hyperbolic distribution, are developed and applied to simulated and real data. Furthermore, these two non-elliptical growth mixture models are extended to accommodate missing values, which are near-ubiquitous in real data. Recently, finite mixtures of non-elliptical distributions have flourished and facilitated the flexible clustering of the data featuring longer tails and asymmetry. However, in practice, real data often have missing values, and so work in this direction is also pursued. A novel approach, via mixtures of the generalized hyperbolic distribution and mixtures of the multivariate skew-t distributions, is presented to handle missing values in mixture model-based clustering context. To increase parsimony, families of mixture models have been developed by imposing constraints on the component scale matrices whenever missing data occur. Next, a mixture of generalized hyperbolic factor analyzers model is also proposed to cluster high-dimensional data with different patterns of missing values. Two missingness indicator matrices are also introduced to ease the computational burden. The algorithms used for parameter estimation are presented, and the performance of the methods is illustrated on simulated and real data. / Thesis / Doctor of Philosophy (PhD)

Cluster analysis is commonly described as the classification of unlabeled observations into groups such that they are more similar to one another than to observations in other groups. Model-based clustering assumes that the data arise from a statistical (mixture) model and typically a group of many models are fit to the data, from which the `best' model is selected by a model selection criterion (often the BIC in mixture model applications). This chosen model is then the only model that is used for making inferences on the data. Although this is common practice, proceeding in this way ignores a large component of model selection uncertainty, especially for situations where the difference between the model selection criterion for two competing models is relatively insignificant. For this reason, recent interest has been placed on selecting a subset of models that are close to the selected best model and using a weighted averaging approach to incorporate information from multiple models in this set. Model averaging is not a novel approach, yet its presence in a clustering framework is minimal. Here, we use Occam's window to select a subset of models eligible for two types of averaging techniques: averaging a posteriori probabilities, and direct averaging of model parameters. The efficacy of these model-based averaging approaches is demonstrated for a family of generalized hyperbolic mixture models using real and simulated data. / Thesis / Master of Science (MSc)