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I need to make linear model for which I need to do Gibbs sampling in MCMC simulations. The model needed to be fitted is a linear mixed model.

Please suggest me for a robust R package for this task.

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The CRAN Task View on Bayesian inference lists several. I recommend arm and MCMCpack. If you can use BUGS then the R2WinBUGS and glmmBUGS will help you fits linear mixed models.

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  • $\begingroup$ I think mcmc doesnot have Gibbs sampling, do it? It does random-walk Metropolis for an arbitrary continuous distribution on R. I could find about gibbs sampling in arm, may be I missed something. The BUGS (Bayesian inference Using Gibbs Sampling) seems to have gibbs sampling facility. thanks for the suggestion. $\endgroup$ – John Nov 27 '11 at 8:14
  • $\begingroup$ It seems that BRugs is delayed for R2.14 Doing Bayesian Data Analysis $\endgroup$ – audijenz Nov 27 '11 at 10:18
  • $\begingroup$ JAGS can also be used with R packages rjags and dclone. If you're running on linux, this might be a simpler solution than R2WinBugs. $\endgroup$ – jbowman Dec 3 '11 at 16:43
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For this task, an efficient new method has recently introduced by Havard Rue and his colleagues at NTNU (JRSSB, 2009, 71(2), 319-392) as called Integrated Nested Laplace Approximation (INLA). INLA substitutes MCMC simulations with accurate, deterministic approximations to posterior marginal distributions. The quality of such approximations is very high, such that even very long MCMC runs could not detect any error in them. An R package (with the same name, INLA) is already available from the web-site www.r-inla.org.

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  • $\begingroup$ is it possible to perform something that "Reversible Jump Sampling" can do, which Allows ‘jumps’ between models with different spaces $\endgroup$ – John Nov 28 '11 at 3:45
  • $\begingroup$ Yohn, no INLA can not do what RJMCMC can do. $\endgroup$ – Gregor Gorjanc Dec 3 '11 at 10:57

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