Abstract

Abstract
The Bayesian Way to Elementary Statistics
;Jeff Gill*, Mary W. Gray*, Monica Jackson
Bayesian statistics has not penetrated undergraduate statistics teaching despite its importance in the rest of the discipline, both academically and professionally. Historically there are two primary reasons for this regrettable state. First, traditional Bayesian inference relied heavily on integral calculus for producing marginal posterior distributions that could be reported in regression tables and elsewhere. After 1990 the emphasis was using Markov chain Monte Carlo for these types of operations, but for some time it required computational expertise and programming skills. Neither of these problems exist today as there now exists easy to use and reliable MCMC software implementations in R packages, STAN, and JAGS. In this work we lay out a detailed plan for replacing the outdated traditional undergraduate introductory statistics course model with a 21st century appropriate version that gives students the modern important skills for data analysis and modeling with an emphasis on prior to posterior inference as a scientific paradigm.

*Jeff Gill is Distinguished Professor, Department of Mathematics and Statistics and
School of Public Affairs, American University, Washington DC
**Mary W. Gray is Distinguished Professor, Department of Mathematics and Statistics,
American University, Washington DC, corresponding author
mgray@american.edu
***Monica Jackson is Professor, Department of Mathematics and Statistics,
American University, Washington DC