Acceptance-Rejection Sampling with Hierarchical Models

• Main Author: Ayala, Christian A
• Format: Others
• Published: Scholarship @ Claremont 2015
• Subjects: bayesian inference; hierarchical model; rejection sampling; perfect simulation; random variate generation; Statistical Models
• Online Access: http://scholarship.claremont.edu/cmc_theses/1162; http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=2165&context=cmc_theses

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.