Bayesian statistics is a simple and unified theory of statistical inference built directly from probability theory. It is generally treated as an advanced subject in statistics, but I think this is inappropriate. Introductory statistics courses in college should use Bayesian statistics in classes designed for engineers and other technical students.

I can think of four significant advantages to teaching Bayesian statistics instead of frequentist statistics to engineering and other technical students:

1. Because Bayesian methods are derived directly from a simple and unified theory of inference technical students will find it easier to learn and retain Bayesian statistics than they would frequentist methods. This will allow students to learn and retain more.
2. Bayesian statistics, generalizes more obviously than frequentist statistics. It is easy for even Bayesian novices to do inference using novel models. Because doing Bayesian statistical inference is conceptually simple, engineers and other practitioners will use statistical analysis where they would otherwise not have and be able to tackle more complex problems than they would otherwise be able to.
3. Bayesian methods can sometimes squeeze more information out of data than frequentist statistics. Bayesian methods perform at least as well as, and sometimes better than, frequentist statistics, even when evaluated by frequentist criteria.
4. The output in Bayesian methods is a subjective probability distribution about the parameters of interest. This makes coming up with errors extremely simple, which is valuable for engineers because it is common in engineering problems for uncertainties to be just as important as point estimates.
5. Bayesian statistics leads naturally into normative decision theory. This makes it easy to give students a technical understanding of what it means to arrive at optimal decisions.

The one problem with Bayesian statistics is that solving problems using Bayesian statistics is frequently computationally expensive. However, there are relatively simple and general numerical techniques that can be used to solve problems. Additionally, engineering students are generally already familiar with using simple simple tools (Microsoft Excel and graphing calculators) to do solve problems numerically.

For historical reasons, despite Bayesian statistics’ advantages over frequentist statistics, most introductory statistics courses use frequentist methods. Until about 15 years ago, computation was expensive enough that it made Bayesian methods impractical for most appliations. Today computation is cheap enough that it is not a barrier to using Bayesian methods, so schools should no longer teach frequentist statistics first.

Happily, there are at least some undergraduate courses that do teach introductory statistics courses using Bayesian statistics, for example at Waikato University in New Zealand. Students will benefit from more schools will adopt the Bayesian perspective for their introductory courses, and I hope that schools do so quickly.

Resources for learning the Bayesian perspective on probability (the very very basics of Bayesian statistics):

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