Interpretation of the Bayesian estimation results


I’m trying to do the Bayesian estimation of the two slightly different versions of the same model and want to compare the results in terms of which version better fits the data that I have. Based on what number can I do this? Log data density or minus the log posterior?
Could you please also explain how to interpret these two numbers correctly?

Thank you a lot for your help!

You would use the marginal data density. For this, both models need to be estimated on the same data. See Koop’s textbook for a very accessible introduction.

Dear Professor Pfeifer,
thank you a lot for your reply and for giving reference to the book! It is really helpful!

As I’m new to the estimation techniques, could you, please, guide me slightly and say, whether there is a way to say statistically that one business cycle decomposition for certain variables like consumption and gdp is better when comparing estimations of the two similar versions of the same model?

Thank you once again for your help, Professor!