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pragmatist comments on The buildup to Jaynes? - Less Wrong Discussion
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This sounds more like a pedagogical issue than an inherent problem with classical statistics. I agree that Bayesianism is philosophically "cleaner", but classical statistics isn't just a hodge-podge of unjustified tools. If you're interested in a sophisticated justification of classical methods, this is a good place to start. I'm pretty sure you'll be unconvinced, but it should at least give you some idea of where frequentists are coming from.