# Questions tagged [gibbs]

The Gibbs sampler is a simple form of Markov Chain Monte Carlo simulation, widely used in Bayesian statistics, based on sampling from full conditional distributions for each variable or group of variables. The name comes from the method being first used on Gibbs random fields modeling of images by Geman and Geman (1984).

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### Sampling variables and calculating likelihood in WinBUGS/OpenBUGS

I am trying to read some WinBUGS/OpenBUGS examples to figure out how to specify models. I can't seem to understand where the probabilistic dnorm, ...
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### Gibbs sampling convergence

In an astronomical context, the authors of a paper desire to use a Gibbs algorithm. Please note: I am inexperience in MCMC algorithms, and specifically in Gibbs sampling. What we want, in essence, is ...
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### Gibbs sampling from conditional full posterior distribution

I am reading the paper by Willemsen et al (2015), "A multivariate Bayesian model for embryonic growth", Statistics in Medicine, 34:8, 1351–1365 where they define the posterior distribution as, \begin{...
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### Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
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### R alternatives to JAGS/BUGS [closed]

I've recently fit more complex hidden markov models with random effects and covariates etc. JAGS was the only program that could get the job done. Now I want to write my own functions to facilitate ...
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### Gibbs sampling and Conjugate Priors

Are conjugate priors required when performing Gibbs sampling?
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### JAGS: posterior predictive distribution

I am fitting a simple linear regression model with R & JAGS: ...
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### When 2% of the Bayesian Model have not converged?

I have model with 20000 latent parameters, set up in a Gibb's sampler. 98% of the parameters and sometimes 99.5% of the parameters satisfy the Geweke convergence statistic, have low autocorrelation ...
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### Derive Marginal Posterior to set up Gibbs-Sampler

I am currently trying to replicate a Hierarchical Model for multivariate returns proposed in the paper Portfolio selection using hierarchical Bayesian analysis and MCMC methods. However, in order to ...
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### Efficiency in Metropolis Vs Gibbs sampling

I have read that Gibbs sampling is more efficient than Metropolis algorithm. Why? Is this due only to the fact the in Gibbs sampling the acceptance rate is $1$, so that the chain needs fewer ...
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### Drawing from a conditional density

I have a simple question. Suppose $X=(X_1,X_2,X_3)$ is multivariate normal. What's the best (quickest) way to draw from the conditional density $X_1\mid \exp(X_1)+\exp(X_2)+X_3$?