Gelman and Rubin

The Gelman-Rubin diagnostic is a method used to check if multiple Markov Chain Monte Carlo (MCMC) simulations have stabilized and are sampling from the same distribution. It compares the variability within each individual chain to the variability between different chains. If the chains have converged, their results should be similar, and this ratio will be close to 1. If not, the ratio is higher, indicating more data is needed for reliable results. This helps ensure that complex statistical models are accurately explored and the estimates are trustworthy.