What problem do these trace plots indicate?

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?

• Are you sure the posterior is a proper distribution? – Sycorax Jul 8 '18 at 1:50
• @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? – KUZ Jul 8 '18 at 21:06
• 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. – Sycorax Jul 8 '18 at 21:09
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.