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).

Filter by
Sorted by
Tagged with
2
votes
1answer
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 $\mu$ ...
5
votes
1answer
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 ...
3
votes
2answers
2k views

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, ...
3
votes
1answer
501 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.
4
votes
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.
2
votes
1answer
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 $X_1\mid \exp(X_1)+\exp(X_2)+X_3$?
4
votes
2answers
772 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 ...
2
votes
0answers
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. ...
91
votes
3answers
53k views

Can someone explain Gibbs sampling in very simple words? [duplicate]

I'm doing some reading on topic modeling (with Latent Dirichlet Allocation) which makes use of Gibbs sampling. As a newbie in statistics―well, I know things like binomials, multinomials, priors, etc.―,...
41
votes
4answers
6k views

OpenBugs vs. JAGS

I am about to try out a BUGS style environment for estimating Bayesian models. Are there any important advantages to consider in choosing between OpenBugs or JAGS? Is one likely to replace the other ...
4
votes
2answers
360 views

Resources about Gibbs sampling in hybrid Bayesian networks

I've been trying to get my hands on a substantial resource for using Gibbs sampling in hybrid Bayesian networks, that is, networks with both continuous and discrete variables. So far I can't say I ...
29
votes
3answers
10k views

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 ...
3
votes
1answer
4k views

JAGS: posterior predictive distribution

I am fitting a simple linear regression model with R & JAGS: ...
1
vote
2answers
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 ...
1
vote
1answer
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 ...
2
votes
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 ...
15
votes
2answers
7k views

Where do the full conditionals come from in Gibbs sampling?

MCMC algorithms like Metropolis-Hastings and Gibbs sampling are ways of sampling from the joint posterior distributions. I think I understand and can implement metropolis-hasting pretty easily--you ...