Different starting values lead to different log data density

[earsmall]

Hi, I am trying to compare two models by comparing log data densities of them.

In the beginning, model A is preferred to model B owing to the fact that
Log data density of A (modified harmonic mean) = -600.503
Log data density of B (modified harmonic mean) = -601.322

However, with different starting values on model A, I got the opposite result of
Log data density of A (modified harmonic mean) = -602.088
Log data density of B (modified harmonic mean) = -601.322

This result says Model B is better than Model A.

One thing strange is with different starting values, modes are same and Laplace approximation are almost similar as well.
Is there any problem in modified harmonic mean?

[jpfeifer]

Marginal data densities are based on approximations. With the same mode, the Laplace approximation must be the same. The modified harmonic mean estimator relies on MCMC draws. The differences you see suggest that there is still to much numerical error and you might need more draws.

That being said, if you follow the criterion in Kass/Raftery (1995): "Bayes Factors", the differences you find are "Not worth more than a bare mention"