Bayesian Computing in the Undergraduate Statistics Curriculum

Abstract

Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in turn, have potentially transformed Bayesian education at the undergraduate level. This article provides an overview of the various options for implementing Bayesian computational methods motivated to achieve particular learning outcomes. For each computational method, we propose activities and exercises, and discuss each method’s pedagogical advantages and disadvantages based on our experience in the classroom. The goal is to present guidance on the choice of computation for the instructors who are introducing Bayesian methods in their undergraduate statistics curriculum. Supplementary materials for this article are available online.

Keywords:

• Bayesian computing
• Bayesian education
• Gibbs sampling
• Just Another Gibbs Sampler (JAGS)
• Markov chain Monte Carlo (MCMC)
• Metropolis sampling

Supplementary Materials

The files JSE_R_supplement_unblinded.Rmd and JSE_R_supplement_unblinded.pdf contain respectively the R Markdown and pdf versions for all of the Bayesian calculations described in this paper. The file atlantic.csv is the data file for the change point example of named storms in Section 4.2. The file UJSE-2019-0165_final_supp.pdf contains descriptions of the four learning activities and the R code for the normal approximation for the two-group logistic example described in Section 2.3.

Acknowledgments

We are very grateful to the editor, the associate editor, and four reviewers for their useful comments and suggestions.

Notes

1 ¹Note that our prior belief has two components. The first prior belief is that the probability that β₁ is within 0.5 is equal to 0.5, and the second prior belief is that little is known about the location of β₁ outside of the interval $(-0.5,0.5)$. A Cauchy density is a better match to this prior information than the normal density since the Cauchy has flatter tails than the normal reflecting lack of knowledge of prior information in the tails.