I don’t see a reason why you can’t do it even if it’s wrong.
If it’s wrong, then it’s not clear what exactly are we doing. If you run out of sample space, there is no way to correct this mistake, because it’s what the sample space means, options still available.
The problem in choice of sample space for Bayesian updating is the same problem as in finding the formalism for encoding a solution to the ontology problem (a preference that is no longer in danger of being defined in terms of misconceptions).
(And if there is no way to define a correct “sample space”, the framework itself is bogus.)
⟨comment deleted; it was this one before I edited it, and somehow got duplicated.⟩
If it’s wrong, then it’s not clear what exactly are we doing. If you run out of sample space, there is no way to correct this mistake, because it’s what the sample space means, options still available.
The problem in choice of sample space for Bayesian updating is the same problem as in finding the formalism for encoding a solution to the ontology problem (a preference that is no longer in danger of being defined in terms of misconceptions).
(And if there is no way to define a correct “sample space”, the framework itself is bogus.)
I believe the above comment is the old edition that should be deleted.