Model Comparison - Bayes Ratio

Estimation ML/Bayesian estimation
#1

Dear all,

I perform a model comparison via the dynare command:

model_comparison (marginal_density=laplace) rob30_model1(0.5) rob30_model2(0.5);

Both models were estimated on slightly different datasets and rob30_model2 contains more estimated parameters. I obtain the following results:

Model Comparison (based on Laplace approximation)
Model rob30_model1 rob30_model2
Priors 0.500000 0.500000
Log Marginal Density 2677.598998 3733.456053
Bayes Ratio 1.000000 Inf
Posterior Model Probability 0.000000 1.000000

Based on this I have two questions:

  1. What’s is the reason that I end up with a Bayes Ratio of 1:0?

  2. In both models the prior distributions have been truncated for the estimation. So this would mean that the model comparison would be invalid anyway, correct?

Thanks for your help and sorry for the basic questions.

Best

Robert

#2

There is a difference of about 50 log points in the marginal data density. That is huge. Model 2 is e^{50} times more likely than model 1. So it is not surprising that model 2 get all the probability if the two probabilities need to add up to 1.

Your comparison is invalid for two reasons:

  1. (Implicit) prior truncation if it differs between models
  2. The fact that the data is not the same across models.
#3

Thanks a lot Johannes!