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I was wondering how statistics and decision theory are related?

It looks to me all the statistics problems/tasks can be formulated in decision theory. Also problems in decision theory can be formulated in statistics/probability problems, or in deterministic way. So is statistics just a part of the problems studied in decision theory?

Or are they just two theories with overlapping and neither falls completely inside the other?

But I have to admit that I don't have a systematic big picture of what topics statistics theory and decision theory are covered respectively, and would like to here some of your point of view.

Thanks and regards!

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Statistical decision theory is a subset of statistical theory.

Exploratory statistics is not decision theory but it is statistics.

A theory about how to make (good) decisions is certainly much wider than statistical decision theory. For example, making a good decision in society may have more relation with psychology or even philosophy than with statistics, don't you think?

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  • $\begingroup$ @robin Of note, the OP mentioned "decision theory" (that you addressed in your last sentence), not "statistical decision theory" (that you're actually using in your first sentence). I do not intend to be punctilious, but we human beings are known to have (and express) limited rationality: In short, we are able to take good (not necessarily optimal) decisions when faced with a limited amount of information, often thanks to abduction--this is not a criticism, just some overt reflexions. (...) $\endgroup$
    – chl
    Apr 5, 2011 at 20:31
  • $\begingroup$ (...) Long ago, Kahneman & Tversky showed that human decisions can depart from rational decisions, or those outcomes predicted by Game Theory, to a great (and somewhat unexpected) extent. $\endgroup$
    – chl
    Apr 5, 2011 at 20:43
  • $\begingroup$ @chl I added "statistical" before decision to make clear that there is a part of statistic that is dedicated to decision theory. Do you think it is false ? (...) $\endgroup$
    – robin girard
    Apr 6, 2011 at 6:02
  • $\begingroup$ @chl I'd love to read Kahneman & Tversky. I'd be glad to see how they define "rational" decision (and departure from it) and more importantly what they call a "great" extent. $\endgroup$
    – robin girard
    Apr 6, 2011 at 6:06
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    $\begingroup$ @robin No, on the contrary. I like the idea of making a distinction between statistical and human decision. My remark was mainly about this, and your last two points are clearly relevant: what is a good decision, and how to characterize any departure from it. (K&T highlighted a lot of judgment biases, but this was really a sidenote.) I'll try to develop this view later. $\endgroup$
    – chl
    Apr 6, 2011 at 7:15

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