I build a Bayesian hierarchical model that is fitted to students’ course data from Maastricht College, a Liberal Arts college. This model is compared to an independent model fitted to each course and a pooled model using the mean squared error from a test set. The models are all fitted with a Gibbs sampler, a popular Markov Chain Monte Carlo algorithm used in Bayesian models. There are certain semi conjugate priors and conditional distributions used to build the models. A Gibbs sampler is used due to its simplicity when building a hierarchical model and its feasibility to sample from the distributions. This study will explore how well the hierarchical model can help predict student course grades using a training and testing set. There will be a prediction for each course that will be used when calculating the mean squared error.
The rest of my research paper is at this link: https://drive.google.com/file/d/1bhQ4iKdVtmqiIy4WDBiitXEWDOcJsEfA/view?usp=sharing