For binary sequence prediction, the next bit is unknown and programs offer competing predictions. Bayes’ rule increases the weight of programs that predicted the observed history well and decreases the weight of those that did not. section 9.1.2
Instead of following only the most trusted program, the Bayes mixture predictor weights all programs’ predictions by their posterior support. This crowd-of-hypotheses approach sits within a tradition of inductive inference traced to Solomonoff’s work in the 1960s. section 9.1.2
