CosmoCoffee

Hi,

I have 2 models and the corresponding CosmoMC chains. I want to find which model is preferred. For that how can I calculate the AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion)? Other than that how can I say which model is preferred?

Sorry for this trivial question. Any help would be great.

Srijita

If you have the same number of parameters in both models then I believe the AIC becomes a straight forward check of the maximum likelihood. If not, then you can compare the two AIC by using the minimise (mode 2 of CosmoMC) to calculate the Maximum Likelihood value of your model and compare that with the usual formula for the AIC. For the BIC, you will need the number of samples as well although its the same process: I would recommend running the minimise routine independently of your chains to find the ML. Of course this isn't the best way to test the comparisons of models and I would recommend (though obviously this is an external code to CosmoMC) something like MultiNest or PolyChord and then calculating the Bayesian evidence and then subsequently the Bayes factor for the two models.

Thank you for the reply and PolyChord suggestion. It is very helpful.

A quick alternative to find the Bayesian evidence without nested sampling is to use the method presented in https://arxiv.org/abs/1704.03472 which is implemented in the MCEvidence code: https://github.com/yabebalFantaye/MCEvidence. However, I'm not sure how reliable it is for a large number of parameters (i.e. a high number of dimensions).