# What is causing autocorrelation in MCMC sampler?

When running a Bayesian analysis, one thing to check is the autocorrelation of the MCMC samples. But I don't understand what is causing this autocorrelation.

Here, they are saying that

High autocorrelation samples [from MCMC] often are caused by strong correlations among variables.

1. I'm wondering what are other causes of high autocorrelation samples in MCMC.

2. Is there a list of things to check when autocorrelation is observed in a JAGS output?

3. How can we manage autocorrelation in a Bayesian analysis? I know that some are saying to thin, but others are saying that it's bad. Running the model for a longer period is another solution, unfortunately costly in time and still affecting in some cases the trace of the samples in the MCMC. Why some algorithm are much more effective in exploring and being uncorrelated? Should we change the initial values for the chain to begin with?

3. If you have decided on the sampler already, and do not have the option of playing around with other samplers, then the best bet would be to do some preliminary analysis to find good starting values and step sizes. Thinning is not generally suggested since it is argued that throwing away samples is less efficient than using correlated samples. A universal solution is to run the sampler for a long time, so that you Effective Sample Size (ESS) is large. Look at the R package mcmcse here. If you look at the vignette on Page 8, the author proposes a calculation of the minimum effective samples one would need for their estimation process. You can find that number for your problem, and let the Markov chain run until you have that many effective samples.