Browsing by Subject "Parameter estimation."
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Item Bayesian approaches to parameter estimation and variable selection for misclassified binary data.(2009-08-26T10:47:02Z) Beavers, Daniel.; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Binary misclassification is a common occurrence in statistical studies that, when ignored, induces bias in parameter estimates. The development of statistical methods to adjust for misclassification is necessary to allow for consistent estimation of parameters. In this work we develop a Bayesian framework for adjusting statistical models when fallible data collection methods produce misclassification of binary observations. In Chapter 2, we develop an approach for Bayesian variable selection for logistic regression models in which there exists a misclassified binary covariate. In this case, we require a subsample of gold standard validation data to estimate the sensitivity and specificity of the fallible classifier. In Chapter 3, we propose a Bayesian approach for the estimation of population prevalence of a biomarker in repeated diagnostic testing studies. In such situations, it is necessary to account for interindividual variability which we achieve through both the inclusion of random effects within logistic regression models and Bayesian hierarchical modeling. Our examples focus on applications for both reliability studies and biostatistical studies. Finally, we develop an approach to attempt to detect conditional dependence parameters between two fallible diagnostic tests for a binary logistic regression covariate in the absence of a gold standard test in Chapter 4. We compare the performance of the proposed procedure to previously published means assessing model fit.Item Brane cosmology in string/M-theory and cosmological parameters estimation.(2009-08-25T16:34:05Z) Wu, Qiang, 1977-; Wang, Anzhong.; Physics.; Baylor University. Dept. of Physics.In this dissertation, I mainly focus on two subjects: (I) highly effective and efficient parameter estimation algorithms and their applications to cosmology; and (II) the late cosmic acceleration of the universe in string/M theory. In Part I, after developing two highly successful numerical codes, I apply them to study the holographical dark energy model and LCMD model with curvature. By fitting these models with the most recent observations, I find various tight constraints on the parameters involved in the models. In part II, I develop the general formulas to describe orbifold branes in both string and M theories, and then systematical study the two most important issues: (1) the radion stability and radion mass; and (2) the localization of gravity, the effective 4D Newtonian potential. I find that the radion is stable and its mass is in the order of GeV, which is well above the current observational constraints. The gravity is localized on the TeV brane, and the spectra of the gravitational Kluza-Klein towers are discrete and have a mass gap of TeV. The contributions of high order Yukawa corrections to the Newtonian potential are negligible. Using the large extra dimensions, I also show that the cosmological constant can be lowered to its current observational value. Applying the formulas to cosmology, I study several models in the two theories, and find that a late transient acceleration of the universe is a generic feature of our setups.Item Remotely sensed hyperspectral image unmixing.(2010-10-08T16:34:43Z) Yang, Zhuocheng.; Farison, James Blair.; Engineering.; Baylor University. Dept. of Electrical and Computer Engineering.Estimating abundance fractions of materials in hyperspectral images is an important area of study in the field of remote sensing. The need for liner unmixing in remotely sensed imagery arises from the fact that the sampling distance is generally larger than the size of the targets of interest. We present two new unmixing methods, both of which are based on a linear mixture model. The first method requires two physical constraints imposed on abundance fractions: the abundance sum-to-one constraint and the abundance nonnegativity constraint. The second method relaxes the abundance sum-to-one constraint as this condition is rarely satisfied in reality and uses the relaxed sum-to-one constraint instead. Another contribution of this work is that the estimation is, unlike many other proposed methods, performed on noise reduced hyperspectral images instead of original images.