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Measures and Probability Distributions
We will now show how the Kolmogorov complexity hierarchy introduced
above translates into an algorithmic prior hierarchy.
Suppose represents the history of our universe up until now.
What is its most likely continuation
? Bayes' theorem yields
is the probability
of , given knowledge of , and
is a normalizing factor.
The most likely continuation is
determined by , the prior probability of .
Now what are the formally describable ways of assigning prior probabilities
to computable universes?
In what follows we will first consider traditional
describable semimeasures on ,
then nontraditional probability distributions on .