The world often isn’t nice enough to give us the steel die.
The point is that the probability with die comes in as frequency (the fraction of initial phase space). Yes, sometimes nature doesn’t give you die; that does not invalidate the fact that there exists probability as objective property of a physical process, as per frequentism (related to how the process maps initial phase space to final phase space); the methods employing subjectivity have to try to conform to this objective property as closely as possible (e.g. by trying to know more about how the system works). The Bayesianism is not opposed to this, unless we are to speak of some terribly broken Bayesianism.
‘Probability of model given the data’ is not well defined,
It’s perfectly well-defined.
Nope. Only the change to probability of model given the data is well defined. The probability itself isn’t. You can pick arbitrary start point.
There’s some theory that gives pretty general conditions under which Bayesian procedures converge to the true answer,
The notion of ‘true answer’ is frequentist....
edit: Recall that the original argument was about the trope of Bayesianism being opposed to frequentism etc. here. The point with Solomonoff induction is that once you declare something like this a source of priors, all math youll be doing should be completely identical to frequentist math (when frequencies are within turing machines fed random tape, and the math is done as in my top level post for die), just as long as you don’t simply screw your math up. The point with die example was that no Bayesianist worth their salt opposes to there being a property of chaotic process, what fraction of initial phase space gets mapped to where, because there really is this property.
The point is that the probability with die comes in as frequency (the fraction of initial phase space). Yes, sometimes nature doesn’t give you die; that does not invalidate the fact that there exists probability as objective property of a physical process, as per frequentism (related to how the process maps initial phase space to final phase space); the methods employing subjectivity have to try to conform to this objective property as closely as possible (e.g. by trying to know more about how the system works). The Bayesianism is not opposed to this, unless we are to speak of some terribly broken Bayesianism.
Nope. Only the change to probability of model given the data is well defined. The probability itself isn’t. You can pick arbitrary start point.
The notion of ‘true answer’ is frequentist....
edit: Recall that the original argument was about the trope of Bayesianism being opposed to frequentism etc. here. The point with Solomonoff induction is that once you declare something like this a source of priors, all math youll be doing should be completely identical to frequentist math (when frequencies are within turing machines fed random tape, and the math is done as in my top level post for die), just as long as you don’t simply screw your math up. The point with die example was that no Bayesianist worth their salt opposes to there being a property of chaotic process, what fraction of initial phase space gets mapped to where, because there really is this property.