A Single Series from the Gibbs Sampler Provides a False Sense of Security
Andrew Gelman, Donald B. Rubin · 1992
Abstract The Gibbs sampler can be very useful for simulating multivariate distributions, but naive use of it can give misleading—falsely precise—answers. An example with the using lattice model demonstrates that it is generally impossibile to assess convergence of a Gibbs sampler from a single sample series. This conclusion also applies to other iterative simulation methods such as the Metropolis algorithm.