What is gibbs sampling?

Gibbs sampling is a popular Markov Chain Monte Carlo (MCMC) algorithm used for sampling from high-dimensional probability distributions. It is named after American statistician Josiah Willard Gibbs.

In Gibbs sampling, the algorithm iteratively samples from the conditional distribution of each variable in the model, given the values of all the other variables. This is done by fixing the values of all variables except one and sampling from the conditional distribution of the unfixed variable.

Gibbs sampling is particularly useful when it is difficult to sample from the joint distribution of all variables but sampling from the conditional distributions is easier. It is commonly used in Bayesian statistics, machine learning, and other fields where sampling from complex probability distributions is required.

One of the advantages of Gibbs sampling is that it does not require knowledge of the normalizing constant of the target distribution, as it only relies on sampling from the conditional distributions. However, Gibbs sampling can be slow to converge, and the choice of conditional distributions can greatly impact the efficiency of the sampling process.

Overall, Gibbs sampling is a powerful and widely used MCMC algorithm for sampling from complex high-dimensional probability distributions.