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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

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
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Description

In this paper, a literature review is presented on the application of Bayesian networks applied in system reliability analysis. It is shown that Bayesian networks have become a popular modeling framework for system reliability analysis due to the benefits that Bayesian networks have the capability and flexibility to model complex

In this paper, a literature review is presented on the application of Bayesian networks applied in system reliability analysis. It is shown that Bayesian networks have become a popular modeling framework for system reliability analysis due to the benefits that Bayesian networks have the capability and flexibility to model complex systems, update the probability according to evidences and give a straightforward and compact graphical representation. Research on approaches for Bayesian network learning and inference are summarized. Two groups of models with multistate nodes were developed for scenarios from constant to continuous time to apply and contrast Bayesian networks with classical fault tree method. The expanded model discretized the continuous variables and provided failure related probability distribution over time.

ContributorsZhou, Duan (Author) / Pan, Rong (Thesis advisor) / McCarville, Daniel R. (Committee member) / Zhang, Muhong (Committee member) / Arizona State University (Publisher)
Created2014
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Description
Optimal experimental design for generalized linear models is often done using a pseudo-Bayesian approach that integrates the design criterion across a prior distribution on the parameter values. This approach ignores the lack of utility of certain models contained in the prior, and a case is demonstrated where the heavy

Optimal experimental design for generalized linear models is often done using a pseudo-Bayesian approach that integrates the design criterion across a prior distribution on the parameter values. This approach ignores the lack of utility of certain models contained in the prior, and a case is demonstrated where the heavy focus on such hopeless models results in a design with poor performance and with wild swings in coverage probabilities for Wald-type confidence intervals. Design construction using a utility-based approach is shown to result in much more stable coverage probabilities in the area of greatest concern.

The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.

The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.
ContributorsHassler, Edgar (Author) / Montgomery, Douglas C. (Thesis advisor) / Silvestrini, Rachel T. (Thesis advisor) / Borror, Connie M. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2015
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Description
Bayesian networks are powerful tools in system reliability assessment due to their flexibility in modeling the reliability structure of complex systems. This dissertation develops Bayesian network models for system reliability analysis through the use of Bayesian inference techniques.

Bayesian networks generalize fault trees by allowing components and subsystems to be related

Bayesian networks are powerful tools in system reliability assessment due to their flexibility in modeling the reliability structure of complex systems. This dissertation develops Bayesian network models for system reliability analysis through the use of Bayesian inference techniques.

Bayesian networks generalize fault trees by allowing components and subsystems to be related by conditional probabilities instead of deterministic relationships; thus, they provide analytical advantages to the situation when the failure structure is not well understood, especially during the product design stage. In order to tackle this problem, one needs to utilize auxiliary information such as the reliability information from similar products and domain expertise. For this purpose, a Bayesian network approach is proposed to incorporate data from functional analysis and parent products. The functions with low reliability and their impact on other functions in the network are identified, so that design changes can be suggested for system reliability improvement.

A complex system does not necessarily have all components being monitored at the same time, causing another challenge in the reliability assessment problem. Sometimes there are a limited number of sensors deployed in the system to monitor the states of some components or subsystems, but not all of them. Data simultaneously collected from multiple sensors on the same system are analyzed using a Bayesian network approach, and the conditional probabilities of the network are estimated by combining failure information and expert opinions at both system and component levels. Several data scenarios with discrete, continuous and hybrid data (both discrete and continuous data) are analyzed. Posterior distributions of the reliability parameters of the system and components are assessed using simultaneous data.

Finally, a Bayesian framework is proposed to incorporate different sources of prior information and reconcile these different sources, including expert opinions and component information, in order to form a prior distribution for the system. Incorporating expert opinion in the form of pseudo-observations substantially simplifies statistical modeling, as opposed to the pooling techniques and supra Bayesian methods used for combining prior distributions in the literature.

The methods proposed are demonstrated with several case studies.
ContributorsYontay, Petek (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Shunk, Dan L. (Committee member) / Du, Xiaoping (Committee member) / Arizona State University (Publisher)
Created2016
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Description
Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the

Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the structure of relationships in the data such as clustered/hierarchical data, b) do not allow or control for missing values present in the data, or c) do not accurately compensate for different data types such as categorical data, then the assumptions associated with the model have not been met and the results of the analysis may be inaccurate. In the presence of clustered
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ContributorsKunze, Katie L (Author) / Levy, Roy (Thesis advisor) / Enders, Craig K. (Committee member) / Thompson, Marilyn S (Committee member) / Arizona State University (Publisher)
Created2016