Solomonoff's theory of inductive inference

Solomonoff's theory of inductive inference is a mathematical theory of induction introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory.

Solonomoff himself proved that this induction is incomputable, but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction".

Solomonoff's induction naturally formalizes Occam's razor by assigning larger prior credences to theories that require a shorter algorithmic description.