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I am looking at a lecture on Bayesian Statistics and Why Bayes it is mentioned that, say the data can be modelled with normal distribution, the frequentist approach is to keep the $\mu$ and $\sigma$ as constants but unknown and the "uncertinity" is determined by capturing the samples multiple times and seeing how they sway. In contrast the Bayesians tackle $\mu$ and $\sigma$ as RV's themselves.

Question: Isn't this pretty much same thing in principle? You can quantify uncertinities themselves by the same formulas that you quantify RV's, so in principle despite the fact that Frequentists saying they constants but associating "uncertanities" to them have same effect as saying they are RV's just like what Bayesians do?

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