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What is the subject of statistics called if the subject is used to studying if a statistical model formulated fit the actual data?

If there are more than one general subject to study this, name all of them.

I was thinking that curve fitting and theory of reliability responsible for that. If so, what else?

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  • $\begingroup$ "Emprical?" Not really a branch of statistics, though. Maybe "a posteriori", usually used in economics, in which a theory is derived from the data, rather than "a priori" in which a theory is posted first, then data is used to validate or invalidate. Hard to list all a posteriori approaches. $\endgroup$
    – Charles Pehlivanian
    Jul 3, 2015 at 21:04

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If you're talking about how well a model fits data (not sure what it would mean to say a "statistic" fits the data), that would be goodness of fit.

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    $\begingroup$ This site has a tag for goodness-of-fit, with nearly 400 questions presently tagged with that topic. $\endgroup$
    – EdM
    Jul 3, 2015 at 21:36

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