Bimodal, convergence and long tail posterior figure

Dear Johannes,

Could you help to have a look at the attached two figures? I ran 4 Million draws to estimate my model.

  1. The posterior figure shows that **psiz ** is bimodal and convergence figure shows it does not converge. I am wondering if this is a problem and do you have some advice on how to deal with it?

  2. In terms of convergence figure, rhoz does Not converge either, right? But I already ran 4 Million, do I need to run more to make it converge? Finding the mode is hard, since only mode_compute=6 works.

  3. In terms of posterior figure, the tails of SE_e_z which is the estimated standard deviation of preference shock , are very long. Would that be a problem?

Many thanks in advance.

Kind regards,
udiag.pdf (23.5 KB)
PriorsAndPosteriors1.pdf (68.7 KB)

Bimodality can happen and if you are sure that the code and estimation is correct, it is a feature, not a bug. Convergence diagnostics will be misleading in this case. The question in this case is how to summarize the posterior distribution as the mean will be meaningless. But the posterior density plots still convey the correct message.

Dear Johannes,

It is quite common to report theoretical moments using posterior mean as calibration of parameters. HOWEVER, if I estimate 5 parameters and 1 of them is bimodal posterior distribution, would be right to calibrate this parameter using Mode while the other 4 parameters using posterior mean to see theoretical moments?

Many thanks,

As long as you make explicit what you are doing, you should be fine. The best way to go according to my opinion is either to use the mode for all parameters (aka Maximum “Likelihood” (actually a posterior)) or the fully Bayesian mean of the statistics that interests you as opposed to the statistic at the mean.