Dear all, I compared four models by the dynare command: model_comparison (marginal_density=laplace). The four models are equaly weighted. My question is, why the Log Marginal Density reported by the command slighty differs from the one reported in the estimation results in the command window in Ma…

How big is the difference? Is it more than rounding?

Hello Johannes: Yes, it is. In fact, in some cases, the ranking of the models I am comparing changes. For example: These are the log densitys of the four models I am comparing that one can see in the command window in Matlab, when all posteriors all displayed too. The “best” model would be M3 (mo…

Are you comparing the right objects? The marginal data density is reported using the Laplace approach and the modified harmonic mean.

Well, I am using this: ESTIMATION RESULTS Log data density is 418.410999. parameters prior mean post. mean 90% HPD interval prior pstdev rho_rrf 0.650 0.6672 0.5117 0.8383 invg 0.1000 rho_mup 0.300 0.2603 0.1718 0…

Please provide the full log-file of that model.

Now I see what you mean. Thank you very much. But, what is exactly the difference between the log data density lkaplace approximation and the other log data density? Log data density [Laplace approximation] is 419.450586. Estimation::mcmc: Multiple chains mode. Estimation::mcmc: Old mh-files succ…

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Model_comparison

Estimation ML/Bayesian estimation

jpfeifer 12 October 2020 09:22 8

See

The log marginal data density in mode_computer=6 ML/Bayesian estimation

Both the Laplace approximation and the modified harmonic mean estimator are ways to compute the marginal data density. As computing the marginal data density involves solving a complicated integral, these two methods for tackling the issue have been proposed. In theory, they should yield identical results as they measure the same thing. In practice, both involve approximations and may yield differing results. It is hard to tell which one to prefer. Footnote 11 of Smets/Wouters (2007) states:

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