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I am familiar with the mechanics with both methods, but don't know what factors I should consider when choosing between these two approaches for adjusting a prior.

I would imagine that, on a case by case basis, one could run posterior predictive checks, compare model complexity, etc. to see which model gives the best simplicity-fitting tradeoff.

But in the general case, how does one make the decision of whether to use non-informative priors vs Empirical Bayes?

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If those are your only two options, then you should use empirical Bayes if and only if you have a hierarchical model. A hierarchical model is when you have multiple parameters $\theta_i$ that are assumed to come from the same prior distribution $p(\theta)$. In this situation, empirical Bayes is a safer choice than setting $p(\theta)$ to be a non-informative prior. If you don't have a hierarchical model, then you can't sensibly learn the prior from data, so the non-informative prior is the better option.

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  • $\begingroup$ Thank you Tom. That is certainly my case (having a hierarchical model). Aside from these two options, MAP-II (i.e. MAP on the the hyperparameters using a prior on the priors) and a full Bayes treatment, is there any other way to adjust or inform the choice of the prior? $\endgroup$ – Amelio Vazquez-Reina Sep 12 '14 at 18:25
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    $\begingroup$ Empirical Bayes is only one of the possible approximations to a full Bayes treatment. There are many other approximation algorithms available, such as Variational Bayes and Expectation Propagation. $\endgroup$ – Tom Minka Sep 12 '14 at 18:33

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