# 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).

334 questions
Filter by
Sorted by
Tagged with
19 views

### Gibbs sampling for simple posterior distribution?

I have a likelihood function, $$p(x) = \theta^{\sum x} (1- \theta)^{n-\sum x}$$ and prior distribution, $$p(\theta) \propto \theta^{\alpha - 1} (1- \theta)^{\beta - 1}$$ then the posterior ...
7 views

### Belief Propagation vs Gibbs Sampling

In general what are the cons and pros of using Gibbs sampling to estimate a complex posterior (assuming we can sample from the conditionals) over belief propagation (using a factor graph)?
15 views

### Markov chain Monte Carlo, Mixing Time

How do you estimate the mixing time for a markov chain? I read somewhere one can use the sum of the auto-correlation coefficients or the sum of the auto-covariance coefficients, but I cannot seem to ...
14 views

### sampling question in Gibbs sampling for a Gaussian mixture model

I have some confusions regarding the Gibbs sampling step for the following mixture model: consider a mixture model of the following generative process: $\theta \sim Dir(\alpha)$ (global hidden ...
42 views

### What's the point of Gibbs Sampling? [duplicate]

I am reading a book on doing Bayesian Data Analysis. I have just learned what the Metropolis Hastings (MH) Algo does, at least in relation to Bayesian Data Analysis. My understanding of the MH Algo ...
18 views

21 views

### Gibb's sampling where target prob distribution is itself a conditional joint distribution - p(x,y|t)

I'm new to Gibb's sampling and need basic guidance. Say p1,p2,q-> are Gaussian variables. p1->q<-p2 and q->x where x is a discrete variable (either 1 or 0). How do I go about Sampling (using ...
23 views

### Assign an error to the parameters of MAP estimate

Through a MCMC Gibbs sampler I obtain $M$ chains of the parameters vector $\mathbf{\theta}$, meaning that each component of $\mathbf{\theta}$ is the value of one parameter at a given iteration. ...
123 views

### GIBBS sampling : do samples for the subset of variables approxiamate the related marginal distribution?

I'm reading the page Gibbs sampling on wikipedia. I really don't understand why the following statement is true. "The marginal distribution of any subset of variables can be approximated by simply ...
23 views

### Is there something wrong with my Bayesian hierarchical spatio-temporal model?

I built a Bayesian spatio-temporal model and one of the parameters to be estimated is the random spatial effects s. The random spatial effect is assigned an intrinsic conditional autoregressive prior (...
82 views

### Is the joint distribution $P_{XY}(x,y)$ determined from the conditionals $P_{X|Y}(x|y)$ and $P_{Y|X}(y|x)$?

For simplicity assume that $X,Y$ are discrete, finite, random variables, with joint distribution $P_{XY}(x,y) = \mathbb{P}(X=x\wedge Y=y)$. Now suppose that we do not know $P_{XY}(x,y)$, but are ...
32 views

27 views

31 views

250 views

### Conditional distribution of $\exp(-|x|-|y|-a \cdot |x-y|)$

I am trying to use Gibbs sampling or Metropolis-Hastings to draw samples from the joint distribution$$f(x,y)\propto\exp(-|x|-|y|-a \cdot |x-y|)$$ For this I need the conditional distributions of $x$ ...