Gelman-Rubin diagnostic

The Gelman-Rubin diagnostic is a method used in statistical computing to check if multiple Markov Chain Monte Carlo (MCMC) simulations have stabilized and are reliably representing a distribution. By running several chains and comparing their results, it assesses whether they have converged to the same distribution. A value close to 1 indicates that the chains agree and the sampling process has likely stabilized, giving confidence in the results. If the value is significantly above 1, more sampling may be needed to ensure accurate estimates. It helps determine when the simulation has effectively "settled down."