Editing Markov chain Monte Carlo (section)

====Overrelaxation====
Overrelaxation is a technique to reduce autocorrelation between successive samples by proposing new samples that are negatively correlated with the current state. This helps the chain explore the posterior more efficiently, especially in high-dimensional Gaussian models or when using Gibbs sampling. The basic idea is to reflect the current sample across the conditional mean, producing proposals that retain the correct stationary distribution but with reduced serial dependence. Overrelaxation is particularly effective when combined with Gaussian conditional distributions, where exact reflection or partial overrelaxation can be analytically implemented.<ref>Piero Barone, Giovanni Sebastiani, and Jonathan Stander (2002). "Over-relaxation methods and coupled Markov chains for Monte Carlo simulation." ''Statistics and Computing'', 12(1), 17–26. [https://doi.org/10.1023/A:1013112103963 doi:10.1023/A:1013112103963]</ref>