Decision theory and Bayesian statistics

This chapter outlines some of our more effective demonstrations for teaching decision theory and Bayesian statistics. Our contribution here is in the tricks used to involve students; the ideas behind most of the demonstrations are well known. The activities serve several purposes, including focusing student attention on difficult conceptual issues that are hard to learn in a lecture or by solving homework problems (e.g., the principle of expected gain and determining the value of a life); alerting students to their cognitive illusions (e.g., the incoherent utilities for money and uncalibrated subjective probability intervals); bringing personal issues into the class (e.g., different areas of knowledge in the subjective probability intervals and personal decision problems); dramatizing counterintuitive results which a student might not realize as counterintuitive; and demonstrating the multiple levels of uncertainty in a Bayesian analysis, as well as the coverage property of posterior intervals.