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Lumifer comments on Approximating Solomonoff Induction - Less Wrong Discussion
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It's deeper than that. Bayesian probability theory is a mathematical law. Anything method that works must be computing an approximation of it. Just like Newtonian mechanics is a very close approximation of relativity. But they are not equivalent.
That is not true. The Bayes equation is mathematically correct. A theory is much wider -- for example, Bayesians interpret probability as a degree of belief -- is that also a mathematical law? You need a prior to start -- what does the "mathematical law" say about priors?