Here are two interesting comments from Andrew Gelman’s blog. I love the idea of starting with decisions. That is what we all have to do, every day. Then, given that we have to make a decision, we all use models. And, given that we all use models, let’s learn to make better models.
I wish we introduced decision theory early. Bayesian thinking let’s you escape the straitjacket of a yes / no mindset that comes with p vales and NHST but it’s somewhat unsatisfactory if there’s a real-world yes-no decision at the end of it all, but the course leaves you hanging about how to make that decision. This is my beef with stat courses whether Bayesian oriented or traditional. Ironically, even as the courses progress to more advanced ones they don’t seem to add much more material on the decision theory side. It’s somewhat of a no mans land that no course wants to tread on.
I’m enamored with the idea of beginning an intro course with the very broad idea of models. People are deeply familiar with models in their daily lives — maps, blueprints, essay outlines, the periodic table of elements, weather forecasts, the little plastic planes you glue together, ships in bottles. This leads into formal ideas like constructs, parameters, distributions, etc. You could also bring in the notion that we all act as amateur scientists all the time. We apply implicit models of events and behavior, like when we plan what we’ll wear tomorrow, or evaluate why an acquaintance is acting strangely, or decide whether a girl likes you or is just being nice. These models are devised by reflecting on the past, tested by observing and asking questions, and revised based on those results. This could lead to introducing the scientific method generally and Bayesian priors in particular.