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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.
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]
Gibbs sampling of a probit model is possible because regression models typically use normal prior distributions over the weights, and this distribution is conjugate with the normal distribution of the errors (and hence of the latent variables Y *). The model can be described as
Josiah Willard Gibbs Born (1839-02-11) February 11, 1839 New Haven, Connecticut, U.S. Died April 28, 1903 (1903-04-28) (aged 64) New Haven, Connecticut, U.S. Nationality American Alma mater Yale College (BA, PhD) Known for List Statistical mechanics Chemical thermodynamics Chemical potential Cross product Dyadics Exergy Principle of maximum work Phase rule Phase space Physical optics Physics ...
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.
The mutual information is used to quantify information transmitted during the updating procedure in the Gibbs sampling algorithm. [37] Popular cost function in decision tree learning. The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.
As an alternative to the EM algorithm, the mixture model parameters can be deduced using posterior sampling as indicated by Bayes' theorem. This is still regarded as an incomplete data problem in which membership of data points is the missing data. A two-step iterative procedure known as Gibbs sampling can be used.