# What is the relation between statistics theory and decision theory?

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!

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?

• @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. (...)
– chl
Commented Apr 5, 2011 at 20:31
• (...) 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.
– chl
Commented Apr 5, 2011 at 20:43
• @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 ? (...) Commented Apr 6, 2011 at 6:02
• @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. Commented Apr 6, 2011 at 6:06
• @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.
– chl
Commented Apr 6, 2011 at 7:15