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Distinction between decision analysis and ‘statistical decision theory’

Michail Fragkias writes,

While reading Chapter 22 of your book, Bayesian Data Analysis (2nd ed.) – I came upon the section on the *Distinction between decision analysis and ‘statistical decision theory’* (p. 543-44) in which you seem quite critical on statistical decision theory suggesting that it is not useful for real decision problems. Actually, I was quite confused with the three paragraphs as I thought that they do not reflect statistical decision theory as I understand it.

A disclaimer: I’m an applied economist by training and recently decided to educate myself in Bayesian statistics and econometrics due to my developing interest in statistical decision theory. Obviously, I started working through your book on Bayesian Data Analysis to get a clear exposition of foundations, but did decide to look ahead at Ch. 22 early on due to my interests. Comparing the content of these paragraphs with the treatment in the 2000 book by French and Rios Insua ‘Statistical Decision Theory’, for example, it seems to me that the core idea of statistical decision theory is misrepresented. Unfortunately, there is though no reference in this section to the original work that is being criticized. On the issue of real examples of usage of statistical decision theory, I’m aware of useful applications in economics, such as the work by Brock, Durlauf and West (http://www.nber.org/papers/w10025)

Am I missing something being new to the field?

My reply: I have not read the book that you cite. I am a big fan of decision analysis and decision theory, though. The thing that I don’t like is so-called “statistical decision theory” in which an “estimator” is chosen based on minimizing some theoretically chosen measure of loss. It’s a relic from the 1940s and 1950s, the idea that choosing a statistical estimator should be treated as a decision problem. The decision analysis that I like is set up with actual losses (dollars, lives, whatever).