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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Test for convergence within Gibbs sampler

I am running a Gibbs sampler for Multivariate Normal times Inverse Wishart posterior distribution with missing data imputation step. I am trying to check if my step of simulating covariance matrices ...
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719 views

Gibbs Sampling for Gaussian Mixtures

Does the Gibbs sampler converge to a global maximum in the presence of multiple modes? For example in case of a Gaussian mixture distribution?
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A good Gibbs sampling tutorials and references

I want to learn how Gibbs Sampling works and I am looking for a good basic to intermediate paper. I have a computer science background and basic statistic knowledge. Anyone has read good material ...
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445 views

Non-conjugate improper uniform priors in Bayesian data analysis: how to handle infinite sums?

I've been working on Griddy Gibbs sampler (paper: Ritter and Tanner) and I've implemented it in R. But I've faced a problem when I started thinking on its uses in other contexts. If I try to use an ...
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2k views

Need help on Gibbs sampling with truncated normal and gamma

I am trying to use Gibbs Sampling to simulate a random sample from a joint distribution $f(\beta ,{{Z}_{1}},...,{{Z}_{75}},{{\lambda }_{1}},...,{{\lambda }_{75}})$, where the fully conditioned ...
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233 views

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 $X_1\mid \exp(X_1)+\exp(X_2)+X_3$?
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2k views

Gibbs sampling from posterior distribution using R

New to MCMC. I have a model, saying $$Y_i=\beta_0+\beta_1x_{i1}+\beta_2x_{i2}+\frac{e_i}{\sqrt{\mu}}$$ where $x_{ij}$ are fixed covariates, $e_i\sim N(0,1)$, $\beta_0$, $\beta_1$, $\beta_2$ and $\mu$ ...
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1k views

Convergence results for block-gibbs sampling?

Suppose you have some complex model you want to sample from by Markov chain Monte Carlo. There are many types of situations where you can divide your variables into, say, two groups, and efficiently ...
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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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2answers
2k views

A robust R package to do MCMC and Gibbs sampling

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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502 views

Prior of multivariate Polya distribution?

Anyone knows a prior (preferably conjugate) to the multivariate Polya distribution? I need it for Gibbs sampling. So if anyone has another idea, I am interested.
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2answers
773 views

Is sequential Bayesian updating an option when using MCMC?

I have an implementation of the Griddy Gibbs sampler, but my observations on which I'm conditioning model parameters are too many in number, thus the likelihood underflows quickly, even with a log ...
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236 views

Mathematical reference for the convergence in distribution of the Gibbs sampler

This question is in some sense the intersection of this question and this question. I have read up on the Gibbs sampler, and am now asking for an introduction to the Gibbs sampler for mathematicians. ...
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1answer
4k views

JAGS: posterior predictive distribution

I am fitting a simple linear regression model with R & JAGS: ...
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1k views

Sampling covariance matrix using Gibbs sampling

I am sampling covariance matrix from a Inverse Wishart distribution. In one dimensional case, after doing sufficient iterations I am taking the mode value for variance (after removing the burn-in ...
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1answer
733 views

Comparison of Slice sampling and Gibbs sampling

To me, the two are similar in the sense that slice sampling is just Gibbs sampling for the uniform distribution over the area under the plot of the density function. Is that right? I was wondering if ...
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549 views

Posterior expression for Gibbs sampling

I am trying to estimate parameters of a two dimensional Normal distribution using Gibbs sampling. While it was very easy transform the posterior equation for mean vector to a single dimension normal ...