Hi Michael,
Thanks a lot for your prompt reply. I understand that things can go south
quickly in high dimension. However, at the moment I am testing the
Multinomial Probit model for a smaller dimension (maximum dimension of
integration is just 8). Further, the data used for estimating the model is
also synthesized.
When I estimate the same model using BFGS algorithm, I recover the
parameter absolutely fine (as I generate the data with known
parameter value). On the other hand, when I estimate the same model using
the same dataset using HMC (both static and NUTS), the recovery is not
good. I don’t sample from the whole trajectory in one iteration of HMC but
rather take the last value and use MH method.
However, even with this, I expected it to perform better than what I am
getting. I will be happy to share my code if you think I am making some
fundamental mistake.
Even though I am not using STAN, I have run the code in both Python and
Gauss. Both store value up to 16 significant digits, so don’t
think floating point/machine precision is an issue here.
Subodh