McAnulty College and Graduate School of Liberal Arts
Bayesian regression, Gibbs sampler, Label switching problem, Latent variables, Mixture models, Two component
In this thesis we develop a two component mixture model to perform a Bayesian regression. We implement our model computationally using the Gibbs sampler algorithm and apply it to a dataset of differences in time measurement between two clocks. The dataset has ``good" time measurements and ``bad" time measurements that were associated with the two components of our mixture model. From our theoretical work we show that latent variables are a useful tool to implement our Bayesian normal mixture model with two components. After applying our model to the data we found that the model reasonably assigned probabilities of occurrence to the two states of the phenomenon of study; it also identified two processes with the same slope, different intercepts and different variances.
Maldonado, H. (2012). Bayesian Regression Inference Using a Normal Mixture Model (Master's thesis, Duquesne University). Retrieved from https://dsc.duq.edu/etd/859