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I was wondering from the view of dividing the topics of statistical theory into inference part and non-inference part, what inference topics and non-inference topics statistical theory is covering?

By inference, I mean the task in logic to reach some conclusion from some premises. Probabilistic inference is a way of logical inference using probability.

Can we say statistical theory is just providing probabilistic ways to accomplish logic inference? Or statistical theory and logic inference are overlapping, but neither falls into the other?

Relating to my previous post regarding decision theory and statistical theory, how are logical inference, decision theory and statistical theory are related together and differ from each other?

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  • $\begingroup$ Interesting, why is the downvote? I wish I could give you some reputation for your explanation. $\endgroup$
    – Tim
    Apr 9, 2011 at 21:56
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    $\begingroup$ Yes, why the downvote? If you're willing to downvote you should have the common decency and confidence to explain why. $\endgroup$
    – cardinal
    Apr 10, 2011 at 14:53
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    $\begingroup$ I upvoted this but I imagine the downvote was because the question covers too many questions eg 1) which parts of statistical theory are "inference" and which "non-inference"; 2) is statistical inference a subset of logical inference; 3) how are logical inference, decision theory and statistical theory related to each other. It would be an impressive answer that covered all of this off (but +1 for the question because I think it is possible for the right statistical philosopher). $\endgroup$
    – Peter Ellis
    Jul 31, 2013 at 7:22

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