Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
Displaying 1 - 4 of 4
Filtering by
- Creators: Reiser, Mark R.
Description
In this era of fast computational machines and new optimization algorithms, there have been great advances in Experimental Designs. We focus our research on design issues in generalized linear models (GLMs) and functional magnetic resonance imaging(fMRI). The first part of our research is on tackling the challenging problem of constructing
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
ContributorsTemkit, M'Hamed (Author) / Kao, Jason (Thesis advisor) / Reiser, Mark R. (Committee member) / Barber, Jarrett (Committee member) / Montgomery, Douglas C. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2014
Description
This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs.
ContributorsKim, Soohyun (Author) / Kao, Ming-Hung (Thesis advisor) / Dueck, Amylou (Committee member) / Pan, Rong (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2017
Description
Functional brain imaging experiments are widely conducted in many fields for study- ing the underlying brain activity in response to mental stimuli. For such experiments, it is crucial to select a good sequence of mental stimuli that allow researchers to collect informative data for making precise and valid statistical inferences at minimum cost. In contrast to most existing studies, the aim of this study is to obtain optimal designs for brain mapping technology with an ultra-high temporal resolution with respect to some common statistical optimality criteria. The first topic of this work is on finding optimal designs when the primary interest is in estimating the Hemodynamic Response Function (HRF), a function of time describing the effect of a mental stimulus to the brain. A major challenge here is that the design matrix of the statistical model is greatly enlarged. As a result, it is very difficult, if not infeasible, to compute and compare the statistical efficiencies of competing designs. For tackling this issue, an efficient approach is built on subsampling the design matrix and the use of an efficient computer algorithm is proposed. It is demonstrated through the analytical and simulation results that the proposed approach can outperform the existing methods in terms of computing time, and the quality of the obtained designs. The second topic of this work is to find optimal designs when another set of popularly used basis functions is considered for modeling the HRF, e.g., to detect brain activations. Although the statistical model for analyzing the data remains linear, the parametric functions of interest under this setting are often nonlinear. The quality of the de- sign will then depend on the true value of some unknown parameters. To address this issue, the maximin approach is considered to identify designs that maximize the relative efficiencies over the parameter space. As shown in the case studies, these maximin designs yield high performance for detecting brain activation compared to the traditional designs that are widely used in practice.
ContributorsAlghamdi, Reem (Author) / Kao, Ming-Hung (Thesis advisor) / Fricks, John (Committee member) / Pan, Rong (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2019
Description
One of the premier technologies for studying human brain functions is the event-related functional magnetic resonance imaging (fMRI). The main design issue for such experiments is to find the optimal sequence for mental stimuli. This optimal design sequence allows for collecting informative data to make precise statistical inferences about the inner workings of the brain. Unfortunately, this is not an easy task, especially when the error correlation of the response is unknown at the design stage. In the literature, the maximin approach was proposed to tackle this problem. However, this is an expensive and time-consuming method, especially when the correlated noise follows high-order autoregressive models. The main focus of this dissertation is to develop an efficient approach to reduce the amount of the computational resources needed to obtain A-optimal designs for event-related fMRI experiments. One proposed idea is to combine the Kriging approximation method, which is widely used in spatial statistics and computer experiments with a knowledge-based genetic algorithm. Through case studies, a demonstration is made to show that the new search method achieves similar design efficiencies as those attained by the traditional method, but the new method gives a significant reduction in computing time. Another useful strategy is also proposed to find such designs by considering only the boundary points of the parameter space of the correlation parameters. The usefulness of this strategy is also demonstrated via case studies. The first part of this dissertation focuses on finding optimal event-related designs for fMRI with simple trials when each stimulus consists of only one component (e.g., a picture). The study is then extended to the case of compound trials when stimuli of multiple components (e.g., a cue followed by a picture) are considered.
ContributorsAlrumayh, Amani (Author) / Kao, Ming-Hung (Thesis advisor) / Stufken, John (Committee member) / Reiser, Mark R. (Committee member) / Pan, Rong (Committee member) / Cheng, Dan (Committee member) / Arizona State University (Publisher)
Created2019