Graduation Year
2015
Date of Submission
4-2015
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Mark Huber
Terms of Use & License Information
Rights Information
© 2015 Christian A. Ayala
Abstract
Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior distribution. The algorithm is both verified and validated, and then finally applied to the given data, with comparisons to the results of different methods.
Recommended Citation
Ayala, Christian A., "Acceptance-Rejection Sampling with Hierarchical Models" (2015). CMC Senior Theses. 1162.
https://scholarship.claremont.edu/cmc_theses/1162
