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I was reading about Empirical Bayesian Methods and came across the following:

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My Question: As this text explains, I have often heard that the priors used in Bayesian Methods should be decided prior to seeing any data - however, it seems that Empirical Bayesian Methods seem to outright go against this and choose priors based on the data. Does anyone know why they do this and what are the advantages/disadvantages of doing this compared to the traditional Bayesian Approach?

References:

Richard Hardy
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stats_noob
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  • I don't think Empirical Bayes is as wild as the description seems. Typically you would specify a hierarchical model with a vague prior on the model parameters $\boldsymbol{\theta}$, and the hyper parameters themselves, $\boldsymbol{\eta}$, would have a vague hyper prior distribution. The data is used to update the hyper priors and this cascades down to the prior for $\boldsymbol{\theta}$. Empirical Bayes just simplifies the process a bit by plugging in a data-dependent point estimate for $\boldsymbol{\eta}$ instead of turning a hyper prior into a data-dependent hyper posterior. – Geoffrey Johnson Dec 18 '21 at 15:16

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