A Simple Data Set Useful for Introducing Sequential Bayesian Estimation and Hierarchical Models

• Activity Number: 570
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Teaching of Statistics in the Health Sciences
• Author(s): Thomas Bradstreet*+
• Keywords: statistical education ; sequential Bayesian estimation ; sequential Baysian prediction ; hierarchical model ; binomial probability ; dataset

Abstract

It is fair to say that the Bayesian approach to scientific reasoning, experimental design, and statistical computing has recently gained an impressive amount of momentum among the statistical and other scientific communities. As a result, there is an increased need for datasets to demonstrate Bayesian methodologies. We provide a dataset of binomial counts from each of 7 studies in healthy subjects evaluating protein levels in cerebrospinal fluid. Each subject in each study was classified as either a success or failure, according to the presence or absence, respectively, of a notably elevated protein level. As data from each study became available, we performed Bayesian posterior and predictive analyses to update the binomial probability of success, and to predict the probabilities of important numbers of successes, such as zero, in future studies. With all the data are in hand, they can also be used to demonstrate Bayesian hierarchical modeling. We hope that this series of data serves students and instructors well in introductory Bayesian statistics courses.