2
$\begingroup$

The following plots are trace plots of 3 variables for MCMC results of a hierarchical Bayes probit model. The plots are fairly linear and seem to grow (or decline) without bound. This looks like a problem that needs to be fixed. But I am unsure of what the issue is. What sort of problem does a linear trace plot usually indicate? enter image description here

enter image description here

enter image description here

$\endgroup$
  • 2
    $\begingroup$ Are you sure the posterior is a proper distribution? $\endgroup$ – Sycorax Jul 8 '18 at 1:50
  • $\begingroup$ @Sycorax, the marginal posteriors on these particular variables do no look proper. The closest form they look like are uniform distributions (but not entirely). Suggestions on what this indicates and remedies? $\endgroup$ – KUZ Jul 8 '18 at 21:06
  • 2
    $\begingroup$ My point is that MCMC requires that the target posterior distribution have finite density. You'll have to work through the math of your actual model to check that this is, indeed, a finite distribution. My guess is just a hunch, though -- could be off-base. $\endgroup$ – Sycorax Jul 8 '18 at 21:09
  • $\begingroup$ Label your axes! $\endgroup$ – AdamO Jul 13 '18 at 15:58
4
$\begingroup$

There is probably an issue with your model. Two issues that could lead to such trace plots are:

  1. (as mentioned in the comments) An improper posterior distribution. Did you impose proper priors?
  2. An issue with identifiability.

For point 2: you have 3 parameters, say $\alpha$, $\beta$ and $\gamma$. If the identifiable parameters are actually $(\frac{\alpha}{\gamma}, \frac{\beta}{\gamma})$, then you might observe such a plot, where the 3 parameters diverge but the ratios (or some other transformation) remain more or less constant. One way to check this would be to start with a simpler model, including only 1 or 2 of your parameters (and keeping the 3rd constant), and checking whether your MCMC behaves better in that situation.

$\endgroup$
  • 1
    $\begingroup$ I do impose normal conjugate priors, so they are proper. However, your suggestion of it being an identification issue is promising-that had not occurred to me. I haven't had a chance to fully try out your suggestion yet, but this could be the issue. Thank you, @RobinRyder. $\endgroup$ – KUZ Jul 14 '18 at 22:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.