I recently went through the slides by Johannes Pfeifer on DSGE estimation (from the Kobe lectures).
I understand that basically the estimation proceeds in three steps:
- Prior specification
- Posterior maximization to find the mode
- Posterior simulation via MCMC to get the entire distribution.
My question is: why do we need to simulate the posterior in step 3? From the mode_check plots, it seems as if we already have the posterior distribution?
In other words, what is the difference between the log-posterior stated in the mode_check plots and the posterior obtained via the MH algorithm. Why is the log-posterior not the one we are actually after?