Identifying posteriors based on MCMC and Laplace post estimation

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,
St├ęphane.

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,
St├ęphane.