Variables that do not converge in winbugs

I conducted a Bayesian analysis in winbugs and then checked the convergence from the history plots. The regression coefficients look stabilized, but the variance parameters don't. I got the number of iteration up to 5000, but it still does not look stabilized. I attached the history plots of a regression coefficient and variances. Can you please tell me what I might be doing wrong? Or is is converged?

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• Ideally, you could provide a reproducible example (code, data pasted in or provided as a supplement) – David LeBauer Mar 6 '13 at 3:36

5000? That's nothing :-) In papers it is usual to use like 200,000. Variance parameters are always the worse for estimation. You have a huge autocorrelation in the chains - you should increase your thin parameter at least 16 times. What is your thin parameter now?