|W. M. (Bill) Bolstad (New Zealand)||email@example.com|
At the present time, frequentist ideas dominate most statistics undergraduate programs, and the exposure to Bayesian ideas in is very limited. Nevertheless, it is well known by professional statisticians that Bayesian methods have superior performance, often even outperforming frequentist procedures evaluated under frequentist criteria. This clearly is a problem for our profession!
In the past, analytic solutions for the Bayesian posterior distributions were only possible in a few cases, and the numerical calculation of the posterior often was not feasible because of lack of computer power. Bayes methods were of limited practical use, despite their theoretical advantages. There are other historical reasons that do not deal with practical issues. Efron (1986) concluded that frequentists had captured the "moral high ground of objectivity" by using emotionally loaded terms such as "unbiased estimators", "most powerful tests", "admissible", for what are actually only mathematical properties. However, I believe the main reason why the frequentist ideas dominate statistics is the lack of exposure to Bayesian ideas in introductory statistics courses.
This is now completely unsatisfactory for our profession. Most of our students are not being introduced to the best methods available. Recent developments in computing power, and the development of Markov chain methods for sampling from the posterior have made Bayesian methods possible, even in very complicated models. While these methods are beyond the scope of an introductory statistics course, it is imperative that we prepare our students for them by getting them to look for the right things.
In this paper I make a proposal for how our profession should deal with this challenge, by giving my answers to the journalistic "who, what, where, when, why, and how" questions about the place of Bayesian Statistics in undergraduate statistical education.
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