I have obtained Bayesian estimation results of DSGE model in Dynare, there are final value of the minus of the log posterior (likelihood) and log data density, I am wondering that what are the differences, does log data density more about moment matching and penalizes complexity (care about all moments with weights controlled by precision), while the minus of the log posterior (likelihood) is more about whether model fits the data(the less negative the better), is a likelihood function in which some parameter variables have been marginalized, and it does not penalize model complexity?
Thank you very much and look forward to hearing from you.
You may want to consult a textbook like Koop (2003). The marginal data density integrates out the parameters. It provides the “likelihood” of the data given the model. In contrast, the log posterior is the “likelihood” of the parameters given the data.
Thank you Johannes, log marginal likelihood and log data density are the same thing in Dynare?