Variance 0 at the mode is propagating to metropolis hasting

Estimation ML/Bayesian estimation
1

Some of my posteriors are very tight around some points, My results can be downloaded from:

drive.google.com/open?id=0B7CeaUeeWSo3VjZ1dFRmbHlVd00

(pag. 70-77).
I think it happens because variance almost 0 at the mode is propagating to metropolis hasting.
Is this result normal or is this a problem and I should be worry. How could I fix this?

I am thinking to modify priors so that they have mean and variance similar to the computed at mode.

Thanks a lot

2

Your MCMC did clearly not converge yet. You may need a lot more draws. How did the mode_check plots look like? And what was the acceptance rate during the MCMC?

3

Dear jpfeifer, I think the mode_check plots looks good and the acceptance rate during the MCMC was stable and near to 35%. I attach my plots.

prometheo_TeX_binder.pdf (1.1 MB)

I suspect I will get Variance 0 after MCMC even if I set more draws, because the Ramdom Walk Metropolis Hasting draws random numbers from nomal distribution with variance based in the mode which is zero for several parameters.

I attach my mod-file and data.

modefile.zip (148.4 KB)

4

Hi Aldo,

Judging from the mode check plots a few parameters are still away from their mode. I’m talking about: rho_i, phi_i, kappa_b, etaf, a22, a13, a21 and a32. I guess you used mode_compute=6, since you are able to estimate the model right after mode finding. If you would have used another mode finding routine you would have ended up with a warning message saying that the hessian matrix at the “mode” is not positive definite. However, under mode_compute=6 you might need a lot more draws later for the MCMC. The explanation for this can be found here . Since you are working with a larger model I would say in the millions.

Best,

Robert

5

Thank you dear Robert,
I am using mode_compute = 5 and the hessian is negative definite, I attached my mod-file.

estimation(
datafile='consolidado',
presample=0,
mode_compute = 5, optim = ('Hessian',2), 
mode_check,
diffuse_filter, 
mh_replic=20000,
mh_drop=0.333, 
mh_nblocks=1,       /
posterior_sampling_method = 'random_walk_metropolis_hastings',
//bayesian_irf, irf=20,
//nograph,
forecast = 12,
tex
)
6

This still suggests a problem in mode-finding. Given the size of your model, debugging this amounts to finding a needle in a haystack. Maybe you should start from a smaller model that works.