| Bayesian methods are valuable for their natural incorporation of prior information and their practical convenience for modeling and estimation. This dissertation develops flexible Bayesian parametric methods for system reliability and Bayesian nonparametric models for community detection.;The Bayesian parametric models proposed allow the assessment of system reliability for multi-component systems simultaneously. We start with a model that considers lifetime data at every component. Then we generalize to a unified framework with heterogeneous information. We demonstrate this unified methodology with pass/fail, lifetime, and degradation data at both the system level and the component level. Further, we propose a Bayesian melding approach to combine prior information from multiple levels.;For community detection, we propose a series of statistical models based on Bayesian nonparametric techniques. These statistical models provide a natural approach for identifying communities in networks using only data on edges. We take advantage of the Bayesian nonparametric approach to include an important feature in our models: the number of communities is an implied parameter of the model, which is therefore inferred during estimation. We also introduce an "Erdős Renyi" group for those nodes that do not belong to communities. Other important aspects of this series of models include increasing flexibility of modeling probabilities for edge presence, linking these probabilities to community sizes, and obtaining communities from posterior samples under a decision theory framework. When presenting our models, we discuss model selection and model checking, which are necessary considerations when applying statistical approaches to real problems. |
