In scenario B, where a random child runs up, I wonder if a non-Bayesian might prefer that you just eliminate (girl, girl) and say that the probability of two boys is 1/3?
In Puzzle 1 in my post, the non-Bayesian has an interpretation that’s still plausibly reasonable, but in your scenario B it seems like they’d be clowning themselves to take that approach.
So I think we’re on the same page that whenever things get real/practical/bigger-picture, then you gotta be Bayesian.
I don’t really see how? A frequentist would just run this a few times and see that the outcome is 1⁄2.
In practice, for obvious reasons, frequentists and bayesians always agree on the probability of anything that can be measured experimentally. I think the disagreements are more philosophical about when it’s appropriate to apply probability to something at all, though I can hardly claim to be an expert in non-bayesian epistemology.
I agree that frequentists are flexible about their approach to try to get the right answer. But I think your version of the problem highlights how flexible they have to be i.e. mental gymnastics, compared to just explicitly being Bayesian all along.
In scenario B, where a random child runs up, I wonder if a non-Bayesian might prefer that you just eliminate (girl, girl) and say that the probability of two boys is 1/3?
In Puzzle 1 in my post, the non-Bayesian has an interpretation that’s still plausibly reasonable, but in your scenario B it seems like they’d be clowning themselves to take that approach.
So I think we’re on the same page that whenever things get real/practical/bigger-picture, then you gotta be Bayesian.
I don’t really see how? A frequentist would just run this a few times and see that the outcome is 1⁄2.
In practice, for obvious reasons, frequentists and bayesians always agree on the probability of anything that can be measured experimentally. I think the disagreements are more philosophical about when it’s appropriate to apply probability to something at all, though I can hardly claim to be an expert in non-bayesian epistemology.
I agree that frequentists are flexible about their approach to try to get the right answer. But I think your version of the problem highlights how flexible they have to be i.e. mental gymnastics, compared to just explicitly being Bayesian all along.