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Description
Accelerated life testing (ALT) is the process of subjecting a product to stress conditions (temperatures, voltage, pressure etc.) in excess of its normal operating levels to accelerate failures. Product failure typically results from multiple stresses acting on it simultaneously. Multi-stress factor ALTs are challenging as they increase the number of experiments due to the stress factor-level combinations resulting from the increased number of factors. Chapter 2 provides an approach for designing ALT plans with multiple stresses utilizing Latin hypercube designs that reduces the simulation cost without loss of statistical efficiency. A comparison to full grid and large-sample approximation methods illustrates the approach computational cost gain and flexibility in determining optimal stress settings with less assumptions and more intuitive unit allocations.
Implicit in the design criteria of current ALT designs is the assumption that the form of the acceleration model is correct. This is unrealistic assumption in many real-world problems. Chapter 3 provides an approach for ALT optimum design for model discrimination. We utilize the Hellinger distance measure between predictive distributions. The optimal ALT plan at three stress levels was determined and its performance was compared to good compromise plan, best traditional plan and well-known 4:2:1 compromise test plans. In the case of linear versus quadratic ALT models, the proposed method increased the test plan's ability to distinguish among competing models and provided better guidance as to which model is appropriate for the experiment.
Chapter 4 extends the approach of Chapter 3 to ALT sequential model discrimination. An initial experiment is conducted to provide maximum possible information with respect to model discrimination. The follow-on experiment is planned by leveraging the most current information to allow for Bayesian model comparison through posterior model probability ratios. Results showed that performance of plan is adversely impacted by the amount of censoring in the data, in the case of linear vs. quadratic model form at three levels of constant stress, sequential testing can improve model recovery rate by approximately 8% when data is complete, but no apparent advantage in adopting sequential testing was found in the case of right-censored data when censoring is in excess of a certain amount.
Implicit in the design criteria of current ALT designs is the assumption that the form of the acceleration model is correct. This is unrealistic assumption in many real-world problems. Chapter 3 provides an approach for ALT optimum design for model discrimination. We utilize the Hellinger distance measure between predictive distributions. The optimal ALT plan at three stress levels was determined and its performance was compared to good compromise plan, best traditional plan and well-known 4:2:1 compromise test plans. In the case of linear versus quadratic ALT models, the proposed method increased the test plan's ability to distinguish among competing models and provided better guidance as to which model is appropriate for the experiment.
Chapter 4 extends the approach of Chapter 3 to ALT sequential model discrimination. An initial experiment is conducted to provide maximum possible information with respect to model discrimination. The follow-on experiment is planned by leveraging the most current information to allow for Bayesian model comparison through posterior model probability ratios. Results showed that performance of plan is adversely impacted by the amount of censoring in the data, in the case of linear vs. quadratic model form at three levels of constant stress, sequential testing can improve model recovery rate by approximately 8% when data is complete, but no apparent advantage in adopting sequential testing was found in the case of right-censored data when censoring is in excess of a certain amount.
ContributorsNasir, Ehab (Author) / Pan, Rong (Thesis advisor) / Runger, George C. (Committee member) / Gel, Esma (Committee member) / Kao, Ming-Hung (Committee member) / Montgomery, Douglas C. (Committee member) / Arizona State University (Publisher)
Created2014
Description
Research methods based on the frequentist philosophy use prior information in a priori power calculations and when determining the necessary sample size for the detection of an effect, but not in statistical analyses. Bayesian methods incorporate prior knowledge into the statistical analysis in the form of a prior distribution. When prior information about a relationship is available, the estimates obtained could differ drastically depending on the choice of Bayesian or frequentist method. Study 1 in this project compared the performance of five methods for obtaining interval estimates of the mediated effect in terms of coverage, Type I error rate, empirical power, interval imbalance, and interval width at N = 20, 40, 60, 100 and 500. In Study 1, Bayesian methods with informative prior distributions performed almost identically to Bayesian methods with diffuse prior distributions, and had more power than normal theory confidence limits, lower Type I error rates than the percentile bootstrap, and coverage, interval width, and imbalance comparable to normal theory, percentile bootstrap, and the bias-corrected bootstrap confidence limits. Study 2 evaluated if a Bayesian method with true parameter values as prior information outperforms the other methods. The findings indicate that with true values of parameters as the prior information, Bayesian credibility intervals with informative prior distributions have more power, less imbalance, and narrower intervals than Bayesian credibility intervals with diffuse prior distributions, normal theory, percentile bootstrap, and bias-corrected bootstrap confidence limits. Study 3 examined how much power increases when increasing the precision of the prior distribution by a factor of ten for either the action or the conceptual path in mediation analysis. Power generally increases with increases in precision but there are many sample size and parameter value combinations where precision increases by a factor of 10 do not lead to substantial increases in power.
ContributorsMiocevic, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2014
Description
Many methodological approaches have been utilized to predict student retention and persistence over the years, yet few have utilized a Bayesian framework. It is believed this is due in part to the absence of an established process for guiding educational researchers reared in a frequentist perspective into the realms of Bayesian analysis and educational data mining. The current study aimed to address this by providing a model-building process for developing a Bayesian network (BN) that leveraged educational data mining, Bayesian analysis, and traditional iterative model-building techniques in order to predict whether community college students will stop out at the completion of each of their first six terms. The study utilized exploratory and confirmatory techniques to reduce an initial pool of more than 50 potential predictor variables to a parsimonious final BN with only four predictor variables. The average in-sample classification accuracy rate for the model was 80% (Cohen's κ = 53%). The model was shown to be generalizable across samples with an average out-of-sample classification accuracy rate of 78% (Cohen's κ = 49%). The classification rates for the BN were also found to be superior to the classification rates produced by an analog frequentist discrete-time survival analysis model.
ContributorsArcuria, Philip (Author) / Levy, Roy (Thesis advisor) / Green, Samuel B (Committee member) / Thompson, Marilyn S (Committee member) / Arizona State University (Publisher)
Created2015
Description
Sound localization can be difficult in a reverberant environment. Fortunately listeners can utilize various perceptual compensatory mechanisms to increase the reliability of sound localization when provided with ambiguous physical evidence. For example, the directional information of echoes can be perceptually suppressed by the direct sound to achieve a single, fused auditory event in a process called the precedence effect (Litovsky et al., 1999). Visual cues also influence sound localization through a phenomenon known as the ventriloquist effect. It is classically demonstrated by a puppeteer who speaks without visible lip movements while moving the mouth of a puppet synchronously with his/her speech (Gelder and Bertelson, 2003). If the ventriloquist is successful, sound will be “captured” by vision and be perceived to be originating at the location of the puppet. This thesis investigates the influence of vision on the spatial localization of audio-visual stimuli. Participants seated in a sound-attenuated room indicated their perceived locations of either ISI or level-difference stimuli in free field conditions. Two types of stereophonic phantom sound sources, created by modulating the inter-stimulus time interval (ISI) or level difference between two loudspeakers, were used as auditory stimuli. The results showed that the light cues influenced auditory spatial perception to a greater extent for the ISI stimuli than the level difference stimuli. A binaural signal analysis further revealed that the greater visual bias for the ISI phantom sound sources was correlated with the increasingly ambiguous binaural cues of the ISI signals. This finding suggests that when sound localization cues are unreliable, perceptual decisions become increasingly biased towards vision for finding a sound source. These results support the cue saliency theory underlying cross-modal bias and extend this theory to include stereophonic phantom sound sources.
ContributorsMontagne, Christopher (Author) / Zhou, Yi (Thesis advisor) / Buneo, Christopher A (Thesis advisor) / Yost, William A. (Committee member) / Arizona State University (Publisher)
Created2015
Description
In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.
ContributorsWallgren, Ross (Author) / Presse, Steve (Thesis advisor) / Armbruster, Hans (Thesis advisor) / McCulloch, Robert (Committee member) / Arizona State University (Publisher)
Created2019
Description
Bayesian Additive Regression Trees (BART) is a non-parametric Bayesian model
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
that often outperforms other popular predictive models in terms of out-of-sample error. This thesis studies a modified version of BART called Accelerated Bayesian Additive Regression Trees (XBART). The study consists of simulation and real data experiments comparing XBART to other leading algorithms, including BART. The results show that XBART maintains BART’s predictive power while reducing its computation time. The thesis also describes the development of a Python package implementing XBART.
ContributorsYalov, Saar (Author) / Hahn, P. Richard (Thesis advisor) / McCulloch, Robert (Committee member) / Kao, Ming-Hung (Committee member) / Arizona State University (Publisher)
Created2019
Description
Phylogenetic analyses that were conducted in the past didn't have the ability or functionality to inform and implement useful public health decisions while using clustering. Models can be constructed to conduct any further analyses for the result of meaningful data to be used in the future of public health informatics. A phylogenetic tree is considered one of the best ways for researchers to visualize and analyze the evolutionary history of a certain virus. The focus of this study was to research HIV phylodynamic and phylogenetic methods. This involved identifying the fast growing HIV transmission clusters and rates for certain risk groups in the US. In order to achieve these results an HIV database was required to retrieve real-time data for implementation, alignment software for multiple sequence alignment, Bayesian analysis software for the development and manipulation of models, and graphical tools for visualizing the output from the models created. This study began by conducting a literature review on HIV phylogeographies and phylodynamics. Sequence data was then obtained from a sequence database to be run in a multiple alignment software. The sequence that was obtained was unaligned which is why the alignment was required. Once the alignment was performed, the same file was loaded into a Bayesian analysis software for model creation of a phylogenetic tree. When the model was created, the tree was edited in a tree visualization software for the user to easily interpret. From this study the output of the tree resulted the way it did, due to a distant homology or the mixing of certain parameters. For a further continuation of this study, it would be interesting to use the same aligned sequence and use different model parameter selections for the initial creation of the model to see how the output changes. This is because one small change for the model parameter could greatly affect the output of the phylogenetic tree.
ContributorsNandan, Meghana (Author) / Scotch, Matthew (Thesis director) / Liu, Li (Committee member) / Biomedical Informatics Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study.
ContributorsMiočević, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Thesis advisor) / Grimm, Kevin (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2017
Description
Brown dwarfs are a unique class of object which span the range between the lowest mass stars, and highest mass planets. New insights into the physics and chemistry of brown dwarfs comes from the comparison between spectroscopic observations, and theoretical atmospheric models. In this thesis, I present a uniform atmospheric retrieval analysis of the coolest Y, and late-T spectral type brown dwarfs using the CaltecH Inverse ModEling and Retrieval Algorithms (CHIMERA). In doing so, I develop a foundational dataset of retrieved atmospheric parameters including: molecular abundances, thermal structures, evolutionary parameters, and cloud properties for 61 different brown dwarfs. Comparisons to other modeling techniques and theoretical expectations from the James Webb Space Telescope (JWST) are made. Finally, I describe the techniques used to improve CHIMERA to run on Graphical Processing Units (GPUs), which directly enabled the creation of this large dataset.
ContributorsZalesky, Joseph (Author) / Line, Michael R (Thesis advisor) / Patience, Jennifer (Committee member) / Groppi, Christopher (Committee member) / Young, Patrick (Committee member) / Bose, Maitrayee (Committee member) / Arizona State University (Publisher)
Created2022
Description
The Bayesian paradigm provides a flexible and versatile framework for modeling complex biological systems without assuming a fixed functional form or other constraints on the underlying data. This dissertation explores the use of Bayesian nonparametric methods for analyzing fluorescence microscopy data in biophysics, with a focus on enumerating diffraction-limited particles, reconstructing potentials from trajectories corrupted by measurement noise, and inferring potential energy landscapes from fluorescence intensity experiments. This research demonstrates the power and potential of Bayesian methods for solving a variety of problems in fluorescence microscopy and biophysics more broadly.
ContributorsBryan IV, J Shepard (Author) / Presse, Steve (Thesis advisor) / Ozkan, Banu (Committee member) / Wadhwa, Navish (Committee member) / Shepherd, Doug (Committee member) / Arizona State University (Publisher)
Created2023