Editing Minimum description length (section)

===Statistical MDL Notation===
Central to MDL theory is the [[one-to-one correspondence]] between code length [[function (mathematics)|functions]] and [[probability distribution]]s (this follows from the [[Kraft–McMillan theorem|Kraft–McMillan inequality]]). For any probability distribution <math>P</math>, it is possible to construct a code <math>C</math> such that the length (in bits) of <math>C(x)</math> is equal to <math>-\log_2 P(x)</math>; this code minimizes the expected code length. Conversely, given a code <math>C</math>, one can construct a probability distribution <math>P</math> such that the same holds. (Rounding issues are ignored here.) In other words, searching for an efficient code is equivalent to searching for a good probability distribution.