The Convergence and Diagnostics (CODA) package is frequently used to evaluate the convergence of MCMC output. It provides several statistical tests to test whether MCMC chains have converged. Many prominent statisticians argue that convergence diagnostics should only be used to flag obvious problems with MCMC convergence, but can't be used to authoritatively tell whether MCMC chains have converged.
Remember that MCMC is an algorithm that generates correlated random numbers according to a particular distribution (in this case, our posterior distribution) only when the stationary distribution has been achieved. Consequently, we need to check the following two things:
- That the stationary distribution has been achieved. This is almost always not that simple, since we can never authoritatively tell whether that distribution has been achieved...
