Wei Dai wrote: > BTW, isn't the justification for universal prediction taken in this paper > kind of opposite to the one you took? The abstract says "The problem, > however, is that in many cases one does not even have a reasonable guess > of the true distribution. In order to overcome this problem ..." Your > papers on the other hand assume that the true distribution can be known > and proposed that it must be the Speed Prior. (Later you said you believe > it is the Speed Prior with probability 1.) Is this still your position?

Well, I prefer to recall my more cautious fallback position - let us just write down the assumptions, and derive the consequences. One does not really have to know the true prior; one just needs an upper bound on its "power". Choose some prior P, and assume the universe is sampled from a prior less dominant than P. Then predictions according to P will be rather accurate. For example, suppose the process computing the universe is not optimally efficient for some reason. As long as the resource postulate holds the true prior cannot dominate the Speed Prior, and S-based predictions will be fine. Juergen