Bayesian Randomized Response as a Class Project

• Activity Number: 301
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Education
• Author(s): Michele DiPietro*+
• Companies: Carnegie Mellon University
• Keywords: statistical education ; Bayesian simulation ; randomized response ; writing across the curriculum

Abstract

"Have you ever been in therapy?" is the question that begins the class project described in this paper. Students are instructed to answer according to a randomized response scheme, and then analyze the resulting data to compare the percentage of U.S. and international students seeing a therapist. The project is informed by current learning and motivational theories so that students can use it to explore topics they are interested in. In particular, because the dataset is rather small, students naturally focus on prior elicitation, issues of identifiability and sensitivity analysis. In addition, because of the lack of a closed form solution, students are forced to apply relevant simulation techniques, including rejection sampling, Metropolis-Hastings algorithm, data augmentation, simulation of Bayes factors, and other model selection criteria. Comparison with surprising frequentist results prompts a reflection of the pros and cons of either approach. Because a goal of the project was clear communication of the results, a key stage was the feedback on an early draft, which often led to better statistics as well as better writing. Students' reactions to the project are included.