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My question is not very technical and more like a discussion but I will be happy to have a technical input for the comparison b/w BIC and ABC.

I am trying to understand and use the best model selection method. I have inferred models using swarm optimisation methods and used AIC for model selection. On the other hand I am also seeing a lot of references and discussions about BIC as well. Apparently, many papers have tried and concluded to use both AIC and BIC as model selection method to select the best models. My question here is, What if I use ABC along with AIC and BIC, how this will effect the results or study in a better way because there will be two Bayesian methods involved for model selection. Secondly, what would be the pros and corns of using ABC along with Bayesian Information criterion as model selection method.

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    $\begingroup$ Neither AIC nor BIC use the Bayesian component of your analysis, hence ABC would be useless in that setting. ABC per se can return a posterior probability of a model in a model choice perspective. This may actually be the most common usage of ABC. $\endgroup$
    – Xi'an
    Commented Jul 10, 2022 at 1:28
  • $\begingroup$ So BIC is only named by Bayesian but it is using the component of Information Criterion right ? then why they call it Bayesian or is it just the name ? $\endgroup$
    – Usman YousafZai
    Commented Jul 10, 2022 at 7:20
  • $\begingroup$ You should check the literature. BIC is based on a Laplace approximation of the likelihood and is independent of the prior. $\endgroup$
    – Xi'an
    Commented Jul 10, 2022 at 14:51

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