Physical Sciences and Mathematics Commons^™

Bayesian Approach To Finding The Most Likely Circuit Structure, Shannon Harms

Graduate Research Theses & Dissertations

Systems, and their reliabilities, depend on the reliabilities of the components that theyare composed of, and in this paper we want to nd the system structure that is the most likely given observed data. Bayesian methods were utilized in order to discover the posterior means, or observed reliabilities, of both the components and the systems. Assuming the serial and parallel system structures have independent components, we calculated system reliabilities based on observed component reliabilities by using the multiplication and addi- tion probability rules. We are then able to expand upon the numerical comparison method through a maximum likelihood analysis that …

Exploring A Bayesian Analysis Of Opinion Dynamics Using The Approximate Bayesian Computation Method, Jessica L. Bishop

Graduate Research Theses & Dissertations

Social media has created a whole new framework in the way we understand ones expression of opinion, and how ones' opinion can influence others. Models of opinion dynamics, such as a probabilistic modeling framework of opinion dynamics over time are given by Abir De, Isabel Valera, Niloy Ganguly, Sourangshu Bhattacharya, and Manuel Gomez Rodriguez in ``Learning and Forecasting Opinion Dynamics in Social Networks." In this paper, we will continue to explore their models, now coming from a Bayesian statistical standpoint, specifically looking at the Approximate Bayesian Computation (ABC) method for the computation of better estimations for the data. We will …

Evaluation Of Epilepsy Surgery Using Bayesian Multinomial Regression, Kacy Danielle Kane

Graduate Research Theses & Dissertations

We are exploring the effectiveness of brain surgeries that are supposed to eliminate or reduce the frequency of seizures in young Epilepsy patients. The long-term effectiveness of brain surgeries is evaluated by ordinal categories and brings longitudinal categorical responses.

Using a Bayesian multinomial regression model we examine the responses by the lobe of brain and other covariates as well as time. To overcome computational difficulties we utilize latent variables for multinomial responses and compare the results with frequentists methods.