# AIC and BIC as Priors - what does this mean?

Hello!

I am working on some Bayesian linear regressions, and I am kind of puzzled by the possibility to choose AIC and BIC as Priors under Advanced Options. I have read the Liang et al., (2008) article from which I understand these priors are derived from, but I still do not fully grasp why they are considered Priors here, typically you think of AIC and BIC as an output criterion that is used for model selection.

I am currently doing analyses where I do not want to punish model complexity, and I understand from my analyses that it is clear that the AIC prior serve my purposes well - but I want to be able to communicate in my article how using the AIC prior is different from well conducting a maximum likelihood calculation and present the actual AIC score.

Thanks,

/Philip

## Comments

Dear Philip,

I guess the priors are implied. BIC is an approximation to the Bayes factor under a specific prior assumption for the model parameters (I believe a multivariate normal mean centered at the MLE but with unit information to set the prior width). The AIC can also be viewed as a Bayesian procedure (but with a strange prior that depends on sample size).

Basically, this is the functionality from the BAS package in R. I think it makes sense to include BIC ('cause of the implied prior structure) but AIC does feel like the odd one out.

As an aside, AIC does punish model complexity -- just less severely than a true Bayesian method.

Cheers,

E.J.