This talk explains in simple terms why Bayesians make decisions by maximizing their posterior expected utility. It starts with what a Bayesian means by "probability," and why the axioms of probability are what they are. Next, it explores conditional probability, and why it is defined as it is. It also explains what utility is, and how maximization of expected utility is a consequence. And finally it justifies maximizing posterior expected utility as an optimal procedure. All spaces are assumed to be finite. There will be sums,but no integrals.
Joseph B. "Jay" Kadane is the Leonard J. Savage Professor of Statistics and Social Sciences at Carnegie Mellon University. He holds a B.A. in mathematics from Harvard University and a Ph.D. in statistics from Stanford University. Before coming to Carnegie Mellon University in 1971, he was at Yale and at the Center for Naval Analysis. He served as department head of CMU Statistics 1972-1981. Kadane is an elected fellow of the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, the Center for Advanced Study in the Behavioral Sciences and the International Society for Bayesian Analysis. He was awarded a Fullbright Fellowship to Chile in 2004. While he became emeritus in 2006, Kadane continues to be active in the department. In 2014, he was awarded the DeGroot Prize for his book, Principles of Uncertainty.