Both theories fit 20 data points. That some of those are predictions is irrelevant, except for the inferences about theory simplicity that result. Since likelihoods are the same, those priors are also the posteriors.
My state of belief is then represented by a certain probability that each theory is true. If forced to pick one out of the two, I would examine the penalties and payoffs of being correct and wrong, ala Pascal's wager.
Both theories fit 20 data points. That some of those are predictions is irrelevant, except for the inferences about theory simplicity that result. Since likelihoods are the same, those priors are also the posteriors.
My state of belief is then represented by a certain probability that each theory is true. If forced to pick one out of the two, I would examine the penalties and payoffs of being correct and wrong, ala Pascal's wager.