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Fang, HaianOptimal estimation of head scan data with generalized cross validation
Master of Science (MS), Ohio University, 1995, Electrical Engineering & Computer Science (Engineering and Technology)

Optimal estimation of head scan data with generalized cross validation

Committee:

Joseph Nurre (Advisor)

Keywords:

Optimal Estimation; Head Scan Data; Generalized Cross Validation

Duncan, Kristin ACase and covariate influence: implications for model assessment
Doctor of Philosophy, The Ohio State University, 2004, Statistics
Statistical models are used to describe collections of data and the processes that generated them. Since models are used to draw conclusions about research questions, it is important to determine if a proposed model is an adequate approximation of the true process. When there are competing models, we ask which of the models provides the best approximation. This research addresses the issue of how to best assess model fit using the approach of cross-validation. We suggest that cross-validation should mimic as closely as possible the intended use of the model. This idea motivates a new way to implement cross-validation, covariate included cross-validation. We show that covariate included cross-validation provides better estimates of model error than traditional cross-validation in the appropriate model setting. We also point out a major di®erence between classical cross-validation and a Bayesian version of crossvalidation; for Bayesian models, the apparent error of the model may be larger than a cross-validatory estimate of error. We give an example where this occurs and provide results indicating when the apparent error will not be larger than the leave-one-out cross-validation estimate of error. The latter part of the dissertation looks at the assessment of item response models used for educational assessment. We implement Bayesian cross-validation for Bayes item response models and show how out-of-sample measures of model fit are particularly relevant for nonparametric item response models.

Committee:

Steven MacEachern (Advisor)

Subjects:

Statistics

Keywords:

Bayesian models; model assessment; cross-validation; item response theory

LAM, CHEN QUINSequential Adaptive Designs In Computer Experiments For Response Surface Model Fit
Doctor of Philosophy, The Ohio State University, 2008, Statistics

Computer simulations have become increasingly popular as a method for studying physical processes that are difficult to study directly. These simulations are based on complex mathematical models that are believed to accurately describe the physical process. We consider the situation where these simulations take a long time to run (several hours or days) and hence can only be conducted a limited number of times. As a result, the inputs (design) at which to run the simulations must be chosen carefully. For the purpose of fitting a response surface to the output from these simulations, a variety of designs based on a fixed number of runs have been proposed.

In this thesis, we consider sequential adaptive designs as an “efficient” alternative to fixed-point designs. We propose new adaptive design criteria based on a cross validation approach and on an expected improvement criterion, the latter inspired by a criterion originally proposed for global optimization. We compare these new designs with others in the literature in an empirical study and they shown to perform well.

The issue of robustness for the proposed sequential adaptive designs is also addressed in this thesis. While we find that sequential adaptive designs are potentially more effective and efficient than fixed-point designs, issues such as numerical instability do arise. We address these concerns and also propose a diagnostic tool based on cross validation prediction error to improve the performance of sequential designs.

We are also interested in the design of computer experiments where there are control variables and environmental (noise) variables. We extend the implementation of the proposed sequential designs to achieve a good fit of the unknown integrated response surface (i.e., the averaged response surface taken over the distributions of the environmental variables) using output from the simulations. The goal is to find an optimal choice of the control variables while taking into account the distributions of the noise variables.

Committee:

WILLIAM NOTZ, PhD (Advisor); THOMAS SANTNER, PhD (Committee Member); ANGELA DEAN, PhD (Committee Member)

Subjects:

Statistics

Keywords:

Cross validation; Gaussian stochastic process model; Kriging; Non-stationary response surfaces; Sequential designs; Adaptive designs; Control and noise variables.

Gummadi, JayaramA Comparison of Various Interpolation Techniques for Modeling and Estimation of Radon Concentrations in Ohio
Master of Science in Engineering, University of Toledo, 2013, Engineering (Computer Science)
Radon-222 and its parent Radium-226 are naturally occurring radioactive decay products of Uranium-238. The US Environmental Protection Agency (USEPA) attributes about 10 percent of lung cancer cases that is `around 21,000 deaths per year’ in the United States, caused due to indoor radon. The USEPA has categorized Ohio as a Zone 1 state (i.e. the average indoor radon screening level greater than 4 picocuries per liter). In order to implement preventive measures, it is necessary to know radon concentration levels in all the zip codes of a geographic area. However, it is not possible to survey all the zip codes, owing to reasons such as inapproachability. In such places where radon data are unavailable, several interpolation techniques are used to estimate the radon concentrations. This thesis presents a comparison between recently developed interpolation techniques to new techniques such as Support Vector Regression (SVR), and Random Forest Regression (RFR). Recently developed interpolation techniques include Artificial Neural Network (ANN), Knowledge Based Neural Networks (KBNN), Correction-Based Artificial Neural Networks (CBNN) and the conventional interpolation techniques such as Kriging, Local Polynomial Interpolation (LPI), Global Polynomial Interpolation (GPI) and Radial Basis Function (RBF) using the K-fold cross validation method.

Committee:

William Acosta (Committee Chair); Vijay Devabhaktuni (Committee Co-Chair); Ashok Kumar (Committee Member); Rob Green (Committee Member)

Subjects:

Computer Science

Keywords:

artificial neural networks; cross-validation; correction based artificial neural networks; prior knowledge input; source difference; space-mapped neural networks; support vector regression; radon; random forest regression

Xiong, JingweiA Penalized Approach to Mixed Model Selection Via Cross Validation
Doctor of Philosophy (Ph.D.), Bowling Green State University, 2017, Mathematics/Mathematical Statistics
A linear mixed model is a useful technique to explain observations by regarding them as realizations of random variables, especially when repeated measurements are made to statistical units, such as longitudinal data. However, in practice, there are often too many potential factors considered affecting the observations, while actually, they are not. Therefore, statisticians have been trying to select significant factors out of all the potential factors, where we call the process model selection. Among those approaches for linear mixed model selection, penalized methods have been developed profoundly over the last several decades. In this dissertation, to solve the overfitting problem in most penalized methods and improve the selection accuracy, we mainly focus on a penalized approach via cross-validation. Unlike the existing methods using the whole data to fit and select models, we split the fitting process and selection into two stages. More specifically, an adaptive lasso penalized function is customized in the first stage and marginal BIC criterion is used in the second stage. We consider that the main advantage of our approach is to reduce the dependency between models construction and evaluation. Because of the complex structure of mixed models, we adopt a modified Cholesky decomposition to reparameterize the model, which in turn significantly reduces the dimension of the penalized function. Additionally, since random effects are missing, there is no closed form for the maximizer of the penalized function, thus we implement EM algorithm to obtain a full inference of parameters. Furthermore, due to the computation limit and moderately small samples in practice, some noisy factors may still remain in the model, which is particularly obvious for fixed effects. To eliminate the noisy factors, a likelihood ratio test is employed to screen the fixed effects. Regarding the overall process, we call it adaptive lasso via cross-validation. Additionally, we demonstrate that the proposed approach possesses selection and estimation consistency simultaneously. Moreover, simulation studies and real data examples are both provided to justify the method validity. At the very end, a brief conclusion is drawn and some possible further improvements are discussed.

Committee:

Junfeng Shang (Advisor); Angela Thomas (Other); Hanfeng Chen (Committee Member); John Chen (Committee Member)

Subjects:

Statistics

Keywords:

linear mixed models; penalized approaches; variable selection; cross validation