Hi,

I want to compare the posteriors of model parameters after estimation using

(i) MCMC

(ii) Laplace approximation

I understand that these are contained in oo_posterior_density in my estimation results. When I open the folder oo_posterior_density_parameter for a particular parameter, it contains two columns of data. I am assuming one of these pertains to MCMC and one to laplace. But I am unable to tell which is what? Can you please tell me how do I identify the two.

Thanks

Steve

Hi,

Laplace approximation is used to compute the marginal posterior density of the data (for model comparison), not for estimating the parameters. If you run a MCMC, `oo_.posterior_density`

, as the name suggests, will contain for each parameter an estimate of the posterior marginal density (using a non parametric kernel estimator). The two columns are the coordinates (x and y axis) of the densities.

Best,

Stéphane.

Thanks Stephanie. Just want to clarify a bit. What do we mean by model comparison here. Is there another marginal posterior density somewhere which has to be compared with what we have in oo_posterior_density?

No. The posterior marginal density of the sample (not of the parameters) is used to compare different models. If we have to pick one model in a collection of models, we choose the one with the highest marginal density of the data (*ie* the one for which the sample is more likely). You will find detailed explanations about this in any textbook of Bayesian econometrics.

Best,

Stéphane.