Likelihood vs marginal likelihood in model comparison

Dear all,

I’m a bit confused about model comparison. I’m estimating with Bayesian methods. As I understand, what Dynare calls data density' is what others callmarginal data density’ or `marginal likelihood’. As such, it discriminates with respect to priors: data density is lower if the posterior is further away from the prior.

However, I’m not interested in discriminating with respect to priors. I’m interested in which model is closer to the data **regardless **of my priors. So, my interested object is (correct me if I’m wrong) likelihood at the posterior mode (or mean) but which is not weighted by prior densities.

In this respect,

  1. can I get the likelihood from Dynare?
  2. what are the two objects in the log-file: `initial/final value of the log posterior (or likelihood)’, and why is the final value with the opposite sign (I think they should have the same sign when starting at optimal initial values).

You can do what you suggest, but there is no theoretical justification for what you are doing. Bayesian model comparison by integrating out the prior allows for comparing non-nested models. In contrast, classical likelihood ratio tests require nested models.

  1. You might have to call dsge_likelihood.m directly
  2. They should be the same posterior, but one of them is minus the posterior. In the unstable version, this has been made explicit.