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This may be a simple question, but I'm at a bit of a loss.

Can I compare AIC to WAIC for the same model, one estimated using general linear models and one using Bayesian estimation?

Or do I need to compare models using the same information criterion?

Motivation for the question:

The glm models are preliminary and ultimately inform the choice of more complex Bayesian models. Given the number of models I am running, I am trying to save some time by using glm where possible.

bashity
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  • I think the answer is negative, but you could fit the frequentist model with a flat prior and compare both models Bayesianly, possibly using WAIC, but definitely not by using a Bayes Factor. – JTH Feb 26 '21 at 02:17
  • Thanks for the comment. Yes there doesn't seem to be a lot of active comparison of AIC to WAIC, so I guess I will just need to quickly re-run all the GLM models using a Bayesian estimator. Not too much of a headache I guess. If you have any official sources or explanation as to why they cannot be compared, would be greatly appreciated. – bashity Feb 26 '21 at 03:13

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