Generally, I think it is safe to say that most people are introduced to statistical inference from a frequentist perspective. Many students in graduate programs in statistics are not taught the basics of the Bayesian paradigm including subjective probability, the modeling of prior beliefs through probability distributions, and posterior and predictive inference. This lack of exposure of students to Bayesian thinking has had a major impact on the growth of the use of Bayesian methods in areas of application. I think it is important to discuss how we can effectively communicate Bayesian ideas in academic and industrial settings and how we can facilitate the spread of Bayesian thinking among applied statisticians. This column will discuss a variety of issues relevant to teaching Bayesian ideas. Here is a short list of some topics, although other suggestions by ISBA members are certainly welcome.
How can one introduce Bayesian thinking in the standard elementary statistics class taught as a service course to non-math majors?
Is it desirable to teach both Bayesian and frequentist thinking in an introductory class?
What topics should be taught in an introductory applied Bayesian course at the graduate level?
What is the role of software in teaching Bayesian inference?
What are effective short courses for teaching Bayesian methodology?
How do we argue that Bayesian inference is superior (at least in some settings) to frequentist inference?
In future columns, I hope to describe Bayesian courses that are currently offered and give reviews of recently published texts and software that will help in communicating Bayes.

Recently (August 1997) a series of articles appeared in the American Statistician on the desirability of introducing Bayesian thinking in the first introductory statistics class taught as a service course to students outside of the mathematics or statistics department. I have taught introductory statistics for over 20 years and I have found it very difficult communicating frequentist thinking to this audience. The notion of a sampling distribution is obscure to students and, more importantly, the students have a hard time understanding the repeated sampling interpretation of confidence. I think Bayesian thinking is very attractive at this level. Thinking in terms of subjective probability is very natural for students and Bayes rule can be taught as a formal mechanism for the natural process of updating one's beliefs about unknowns when more information is observed. Currently Alan Rossman and I are writing a beginning statistics text that introduces inference from a Bayesian viewpoint. The first half of the test focuses on data analysis. The second half introduces probability basics -- the focus is on the interpretation of discrete probability tables for one and two variables. Inference is first introduced for categorical models using Bayes rule. A two-way table, a ``Bayes box" (hypothetical counts classified by models and data), is used to teach Bayes rule. We then have chapters on inference for one and two proportions and a normal mean. We focus on the use of discrete priors for unobservables, since these are easier to assess and interpret and it avoids any use of calculus. One innovative aspect of this text is that it essentially is a collection of activities that students work on in class in small groups. Currently we are using this material at Bowling Green for five sections a semester. I think the course is successful in getting across the big ideas in inference (population, samples, confidence in making inference) and the student is well prepared to take a second statistics class on methodology. Unfortunately, there are very few elementary statistics texts currently available that use Bayesian thinking. One text of note is Don Berry's text ``Statistics: A Bayesian Perspective". I have used Don's text both at Duke and Bowling Green with success and I would recommend it for anyone who is teaching a one semester introductory class. Don's text has been very influential in my thinking about teaching elementary Bayes.
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