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Gibbs sampling is named after the physicist Josiah Willard Gibbs, in reference to an analogy between the sampling algorithm and statistical physics.The algorithm was described by brothers Stuart and Donald Geman in 1984, some eight decades after the death of Gibbs, [1] and became popularized in the statistics community for calculating marginal probability distribution, especially the posterior ...
Bayesian inference using Gibbs sampling (BUGS) is a statistical software for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods. It was developed by David Spiegelhalter at the Medical Research Council Biostatistics Unit in Cambridge in 1989 and released as free software in 1991.
Just another Gibbs sampler (JAGS) is a program for simulation from Bayesian hierarchical models using Markov chain Monte Carlo (MCMC), developed by Martyn Plummer. JAGS has been employed for statistical work in many fields, for example ecology, management, and genetics.
Gibbs sampling can be viewed as a special case of Metropolis–Hastings algorithm with acceptance rate uniformly equal to 1. When drawing from the full conditional distributions is not straightforward other samplers-within-Gibbs are used (e.g., see [7] [8]). Gibbs sampling is popular partly because it does not require any 'tuning'.
The Metropolis-Hastings algorithm sampling a normal one-dimensional posterior probability distribution.. In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.
OpenBUGS is the open source variant of WinBUGS (Bayesian inference Using Gibbs Sampling). It runs under Microsoft Windows and Linux, as well as from inside the R statistical package. Versions from v3.0.7 onwards have been designed to be at least as efficient and reliable as WinBUGS over a range of test applications. [1]
When sampling from a full-conditional density is not easy, a single iteration of slice sampling or the Metropolis-Hastings algorithm can be used within-Gibbs to sample from the variable in question. If the full-conditional density is log-concave, a more efficient alternative is the application of adaptive rejection sampling (ARS) methods.
Particularly notable works include: the development of the Gibbs sampler, proof of convergence of simulated annealing, [8] [9] foundational contributions to the Markov random field ("graphical model") approach to inference in vision and machine learning, [3] [10] and work on the compositional foundations of vision and cognition. [11] [12]