A formal theory of inductive inference. Part II

摘要: 1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is extrapolation a very long sequence symbols—presumably containing all information to be used induction. Almost all, if not problems can put this form. Some strong heuristic arguments have been obtained for equivalence last three models. One these equivalent Bayes formulation, priori probabilities assigned sequences symbols on basis lengths inputs universal Turing machine that required produce interest as output. Though it seems likely, certain whether first other three. Few rigorous results presented. Informal investigations made properties There discussions their consistency and meaningfulness, degree independence exact nature used, accuracy predictions comparison those methods. II applied solution problems—prediction Bernoulli sequence, kind Markov chain, use phrase structure grammars some approximations treated most rigorously. The result Laplace's rule succession. second uses less approximations, but discussed, fairly independent approximations. third application, using grammars, least First formal appears deficiencies, hoped presentation admittedly inadequate model will suggest acceptable improvements it. This then an approximate way determination “optimum” grammar given set strings. plausible, subject uncertainties approximation used.