Gibbs Sampling

Glossary

Gibbs Sampling:

One of a number of computational methods collectively known as Markov chain Monte Carlo (MCMC) methods. In simulating a Markov chain, Gibbs sampling can be viewed as a special case of the Metropolis-Hastings algorithm. In statistical practice, the terminology Gibbs sampling most often refers to MCMC computations based on conditional distributions for the purpose of drawing inferences in multiparameter Bayesian models

Bayesian Inference:

Consider the parameter θ of a probability model as a random variable with the prior density function p(θ). The choice of a prior distribution may be based on previous experience or personal opinion. Then Bayesian inference combines information in the observed data x with information provided by the prior distribution to obtain a posterior distribution p(θ|x). The parameter θ may be a vector.

The likelihood function p(x|θ) is defined (up to a constant multiple) as the joint density function of the data x, now viewed as a...