I agree with you that MacKay’s Chi-squared example fails to criticize frequentist best practice. That said, all of the improvements you suggest seem to me to highlight the problem—you have lots of tools in the toolbox, but only training and subjective experience can tell you which ones are most appropriate. On the question of “which approach is more subjective?”, the frequentist advantage is illusory. (On the question of “which approach has the best philosophical grounding?” I go with the Cox theorems.)
Paul Gowder,
I agree with you that MacKay’s Chi-squared example fails to criticize frequentist best practice. That said, all of the improvements you suggest seem to me to highlight the problem—you have lots of tools in the toolbox, but only training and subjective experience can tell you which ones are most appropriate. On the question of “which approach is more subjective?”, the frequentist advantage is illusory. (On the question of “which approach has the best philosophical grounding?” I go with the Cox theorems.)