Dear stan community,

I am new to Bayesian modeling, so my question might be obvious.

I have a model where I try to fit a model that describes and predict the factors correlated with crime in a city. Often, I have to compare different models. When they are predictive, I know that I should rely on exact K-fold Cross-validation or PSIS-LOO.

What should I use in descriptive models, AKA when I am not interested in out-of-sample predictions? I The metric should account for the number of parameters… In linear models I would use the in-sample adjusted-R^2, but what about non-linear? Is there something “bayesian”?

Thanks!