Editing Markov chain Monte Carlo (section)

====Parameter blocking====
Parameter blocking is a technique that reduces autocorrelation in MCMC by updating parameters jointly rather than one at a time. When parameters exhibit strong posterior correlations, one-by-one updates can lead to poor mixing and slow exploration of the target distribution. By identifying and sampling blocks of correlated parameters together, the sampler can more effectively traverse high-density regions of the posterior.

Parameter blocking is commonly used in both Gibbs sampling and Metropolis–Hastings algorithms. In blocked Gibbs sampling, entire groups of variables are updated conditionally at each step.<ref>Óli Páll Geirsson, Birgir Hrafnkelsson, and Helgi Sigurðarson (2015). "A Block Gibbs Sampling Scheme for Latent Gaussian Models." arXiv preprint [arXiv:1506.06285](https://arxiv.org/abs/1506.06285).</ref> In Metropolis–Hastings, multivariate proposals enable joint updates (i.e., updates of multiple parameters at once using a vector-valued proposal distribution, typically a multivariate Gaussian), though they often require careful tuning of the proposal covariance matrix.<ref>Siddhartha Chib and Srikanth Ramamurthy (2009). "Tailored Randomized Block MCMC Methods with Application to DSGE Models." *Journal of Econometrics*, 155(1), 19–38. [https://doi.org/10.1016/j.jeconom.2009.08.003 doi:10.1016/j.jeconom.2009.08.003]</ref>