I use Gelman-Rubin statistics, trace plots, autocorrelation plots and effective sample size to check the convergence. However, I got very different results from the above tests. The Gelman-Rubin statistics are below 1.05 but the effective sample size is quite small, only 200 for each parameter (burn-in 50000, iter 100000). And the autocorrelation plot shows the parameters are highly correlated. I tried to thin the chains but the result is worse. I have the following questions:
- What should I do to improve the effective sample size?
- Can I neglect the effective sample size and conclude the chains have converged?