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- All Subjects: Bayesian statistical decision theory
- Creators: Pan, Rong
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 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
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 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.
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
Description
Healthcare operations have enjoyed reduced costs, improved patient safety, and
innovation in healthcare policy over a huge variety of applications by tackling prob-
lems via the creation and optimization of descriptive mathematical models to guide
decision-making. Despite these accomplishments, models are stylized representations
of real-world applications, reliant on accurate estimations from historical data to jus-
tify their underlying assumptions. To protect against unreliable estimations which
can adversely affect the decisions generated from applications dependent on fully-
realized models, techniques that are robust against misspecications are utilized while
still making use of incoming data for learning. Hence, new robust techniques are ap-
plied that (1) allow for the decision-maker to express a spectrum of pessimism against
model uncertainties while (2) still utilizing incoming data for learning. Two main ap-
plications are investigated with respect to these goals, the first being a percentile
optimization technique with respect to a multi-class queueing system for application
in hospital Emergency Departments. The second studies the use of robust forecasting
techniques in improving developing countries’ vaccine supply chains via (1) an inno-
vative outside of cold chain policy and (2) a district-managed approach to inventory
control. Both of these research application areas utilize data-driven approaches that
feature learning and pessimism-controlled robustness.
innovation in healthcare policy over a huge variety of applications by tackling prob-
lems via the creation and optimization of descriptive mathematical models to guide
decision-making. Despite these accomplishments, models are stylized representations
of real-world applications, reliant on accurate estimations from historical data to jus-
tify their underlying assumptions. To protect against unreliable estimations which
can adversely affect the decisions generated from applications dependent on fully-
realized models, techniques that are robust against misspecications are utilized while
still making use of incoming data for learning. Hence, new robust techniques are ap-
plied that (1) allow for the decision-maker to express a spectrum of pessimism against
model uncertainties while (2) still utilizing incoming data for learning. Two main ap-
plications are investigated with respect to these goals, the first being a percentile
optimization technique with respect to a multi-class queueing system for application
in hospital Emergency Departments. The second studies the use of robust forecasting
techniques in improving developing countries’ vaccine supply chains via (1) an inno-
vative outside of cold chain policy and (2) a district-managed approach to inventory
control. Both of these research application areas utilize data-driven approaches that
feature learning and pessimism-controlled robustness.
ContributorsBren, Austin (Author) / Saghafian, Soroush (Thesis advisor) / Mirchandani, Pitu (Thesis advisor) / Wu, Teresa (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2018
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 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.
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