  Solomonoff completed the Bayesian framework by providing a rigorous, unique,
formal, and universal choice for the model class and the prior. We discuss in
breadth how and in which sense universal (non-i.i.d.) sequence prediction
solves various (philosophical) problems of traditional Bayesian sequence
prediction. We show that Solomonoff's model possesses many desirable
properties: Fast convergence and strong bounds, and in contrast to most
classical continuous prior densities has no zero p(oste)rior problem, i.e. can
confirm universal hypotheses, is reparametrization and regrouping invariant,
and avoids the old-evidence and updating problem. It even performs well
(actually better) in non-computable environments.
