Ray Solomonoff invented the concept of Algorithmic Probability, which formalizes the idea of Bayesian reasoning using information theory, using ideas which have subsequently become known within Kolmogorov complexity theory. In particular, the prior probability of some data is defined as sum( i = 1, infinity, 2^(-Li) ) where Li is the length of the i th description of the data to some universal Turing machine. Algorithmic Probability employs these concepts to identify a posterior probability distribution in ways formally related to Bayesian methods.
These ideas have been subsequently developed by many, including Wallace in Minimum Message Length (MML) inference and Rissanen in Minimum Description Length (MDL) inference.
Solomonoff's subsequent interest has been the application of Algorithmic Probability to the design of very intelligent machines.
Solomonoff, R.J. (1964) "A Formal Theory of Inductive Inference I and II" Information and Control, 7, 1-22 & 224-254.
Solomonoff, R.J. (1978) "Complexity-Based Induction Systems: Comparisons
and Convergence Theorems," IEEE Trans on Info Theory, vol IT-24,