Gibbs sampler

Gibbs sampling is a special case of MH algorithms. Gibbs sampling involves sampling from the conditional distributions of the variables of interest given the values of the other variables until the chain converges to a stationary distribution. Gibbs sampling is very useful for inference under linear models (the prior, the likelihood, and the posterior are all normal distributions) ^[1] and for sampling from high-dimensional distributions. However, it requires the knowledge of conditional distributions.

Let's understand Gibbs sampling by some R codes ^[2]

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1. Z. Yang. Molecular Evolution: A Statistical Approach. Oxford Univ. Press, 2014. ↩︎

2. http://www2.stat.duke.edu/~rcs46/modern_bayes17/lecturesModernBayes17/lecture-7/07-gibbs.pdf ↩︎