Editing Statistical inference (section)

====Minimum description length====
{{Main|Minimum description length}}

The minimum description length (MDL) principle has been developed from ideas in [[information theory]]<ref name="Soofi 2000 1349–1353">Soofi (2000)</ref> and the theory of [[Kolmogorov complexity]].<ref name=HY>Hansen & Yu (2001)</ref> The (MDL) principle selects statistical models that maximally compress the data; inference proceeds without assuming counterfactual or non-falsifiable "data-generating mechanisms" or [[probability models]] for the data, as might be done in frequentist or Bayesian approaches.

However, if a "data generating mechanism" does exist in reality, then according to [[Claude Shannon|Shannon]]'s [[source coding theorem]] it provides the MDL description of the data, on average and asymptotically.<ref name=HY747>Hansen and Yu (2001), page 747.</ref> In minimizing description length (or descriptive complexity), MDL estimation is similar to [[maximum likelihood estimation]] and [[maximum a posteriori estimation]] (using [[Maximum entropy probability distribution|maximum-entropy]] [[Bayesian probability|Bayesian priors]]). However, MDL avoids assuming that the underlying probability model is known; the MDL principle can also be applied without assumptions that e.g. the data arose from independent sampling.<ref name=HY747/><ref name=JR>Rissanen (1989), page 84</ref>

The MDL principle has been applied in communication-[[coding theory]] in [[information theory]], in [[linear regression]],<ref name=JR/> and in [[data mining]].<ref name=HY/>

The evaluation of MDL-based inferential procedures often uses techniques or criteria from [[computational complexity theory]].<ref>Joseph F. Traub, G. W. Wasilkowski, and H. Wozniakowski. (1988) {{page needed|date=June 2011}}</ref>