Marco
Concerning the chain convergence to ergodicity, I think you are right theoretically. However, I have compared two chains of length 120.000 for a model with 63 params. What surprised me is that the correlation is always significant for all parameters even for the last mat file saved.
this may be worth investigating independently
This may not be a general result and indeed I should take a smaller model so that convergence to ergodic would be much quicker.
However, wouldn't we get a better exploration of the posterior distribution, if we initialize the seeds in different chains to a different state, in addition to using a different starting point? Of course, always keeping a clear criterion for doing that to allow for reproducibility?
For sure, we don't want to use the same sequence where one draw in one chain would always be the same as the draw k iterations later in another chain, with k small.
Best
Michel
In the meantime I have seen your other e-mails. Thanks a lot for looking into this.
best Marco
On 8/29/2012 9:54 AM, Michel Juillard wrote:
Hi Marco,
On 08/29/2012 09:38 AM, Marco Ratto wrote:
Dear All,
I am doing some work with metropolis and I noted that the seeds for parallel chains are initialized at the same status,
what do you mean by "same status" ?
so that the chains only differ by the first point,
if the first point is different, is it not that the entire sequence is different (and not an obvious deterministic function of the other sequences?)
but the random sequences are the same: this implies that sequences for each parameter from different chains are correlated (just compare the values from different blocks stored in files _mhxx_blck1.mat _mhxx_blck2.mat).
I would expect initial (positive or negative, depending on initial values of the parameters) correlation while the chains converge from initial conditions towards the ergodic distribution.
Best
Michel
I am wandering if this is on purpose or this behavior is not desirable.
best Marco
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