Convergence Diagnostic: univariate vs multivariate

Estimation ML/Bayesian estimation
1

hi Everyone

After finding the mode by using mode_compute=7, then I obtains 800,000 draws from the Metropolost-Hasting Agorithm.
However, the convergence diagnostic is mixed (Brook and Gelman, 1998).

In particular, I need to estimate 43 parameters. The estimation is fince if there does not exists convergence problem.
However, I have a look at a univariate convergence diagnostic as pdf file, there is a difference between blue line and red line in the figure of parameters of rx and ry. Moreover, these two line are not stable and horizontal. it implies that these two parameters donot convergence.

At the same time, I have a look at the multivariate convergence diagnostic, then I see that the blue line and red line are stable and horizontal. Moreover, there is no gap between these two lines. It implies that there is no multivariate convergence diagnostic

So, my question is whether my estiamted result is accepted for convergence?
Multivariate Convergence diagnostic.pdf (11.4 KB)
Univariate Convergence Diagnostic.pdf (24.8 KB)

2

Use the

command in Dynare 4.5 to see whether the MCMC for these parameters looks good.

3

Dear Prof. Pfeifer

Thank you so much indeed for your suggestion

4

Dear Phuong,

Looking at the multivariate plots, I would not say that the curves are horizontal. I see a (slightly) decreasing slope.

You need to do integration in a space of dimension 43 (the number of parameters) to compute the posterior moments of the estimated parameters. If you think a minute about the problem of filling an hypercube of such a dimension, clearly 800000 cannot be enough.

best,
Stéphane.

5

Dear Stephane

Thank you a lot for that

I got your idea about number of draws. I also remember your explanation about how to choose number of draws for the MH at the Dynare Summer School 2017 in Paris