A generalized characterization of algorithmic probability
Abstract
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the infinite strings. It is shown in this paper that the class of a priori semimeasures can equivalently be defined as the class of transformations, by all compatible universal monotone Turing machines, of any continuous computable measure in place of the uniform measure. Some consideration is given to possible implications for the prevalent association of algorithmic probability with certain foundational statistical principles.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.05733
 Bibcode:
 2015arXiv150805733S
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Logic