Greater divergence with more iterations

[jkropko]

Hi,
I'm seeing a strange behavior with my rstan script.  If I run stan for 100 iterations, I see that a particular parameter is nearly converged, with an R-hat of about 1.1.  But if I go to 1000 iterations the R-hat balloons to over 2, and if I go to 10000 iterations the R-hat is over 3.  Does this mean that the early "convergence" is an illusion?  I don't think the model is unidentified, so I also don't understand why the parameter would diverge to a greater extent after so many iterations.  Have you seen this behavior before in any similar situations?
Thanks,
Jon

[jkropko]

If it helps, the parameter is the r parameter (number of failures until the experiment is stopped) of a negative binomial distribution.

[Michael Betancourt]

Jon,

Does the trace plot look good and then all of a sudden freeze for a long period of time? This can happen when you have a region of low probability mass where the chain gets stuck -- because of detailed balance if it's rare to transition there it's rare to transition back. If you can track down where the chain is getting stuck you might be able to tweak your model a bit to make the transition easier and consequently less probable to get you stuck.

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[Andrew Gelman]

This can happen.  It happened with me with the pre-Matt-trick version of the 8 schools model.  One way to get things moving would be to assign the parameter a strong prior distribution and check that all is going ok, then relax the prior if necessary.

This should also motivate us to work on implementing the Cook/Gelman/Rubin "self-cleaning oven," which should be doable now that we have implemented forward simulation in the transformed parameters block.

A

[jkropko]

Thank you for the reply Michael.  The traceplot looks good, with all of the chains drawing around a mean of about 2 with roughly equal noise.  But then one chain suddenly spikes to about 6 and stays there.  Is there anything I can do to prevent this behavior?  A stronger prior maybe?

[jkropko]

Here is the traceplot.

On Monday, June 24, 2013 2:33:41 PM UTC-4, Michael Betancourt wrote:

[Marcus Brubaker]

This behaviour typically suggests that your posterior has multiple modes.  A stronger prior could help alleviate this.  Alternatively, longer simulations may be useful if the stronger priors are inappropriate or undesirable.

One thing that is suspicious to me is that the jump seems to happen immediately after the warmup period ends.  What version of Stan are you using?  Have you looked at the stepsizes that it's using?

Cheers,

Marcus

[Michael Betancourt]

It could be multiple modes, but if the posterior density at 6 is small then it's a tail/detailed-balance issue. A stronger prior should help to lighten the tail.