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This seems like a nice explanation of Bayes rule and of some parts of statistics that are often not well-presented and lead to confusion. But Bayesian inference is more than just Bayes rule. I dont see any discussion of the idea of probability as subjective belief in there, which is the core of a Bayesian view of probability. Bayes rule is just the machinery for updating beliefs, and as important as that is, frequentists use it too. Bayes rule only gains the huge significance when you have committed to the idea of probability as expressing degree of belief, and which makes you free to put probability distributions over parameters