# 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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### Gibbs Sampler for mixture models: shall I skip some samples to avoid to use correlated samples? [duplicate]

I am implementing a Gibbs sampler in order to estimate the parameters of a mixture model. Assuming that the parameters are contained in a vector $\theta$ what I will do is: Implement and run the ...
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### bayesian decision making - comparing expected loss

The problem is like this: Suppose that I am considering which country should I invest on, country A and country B, based on their GDP growth rate $\alpha$. There are two possible choices for each ...
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### Conditional distribution in this Gaussian Mixture Model

Say I observe $N$ observations $\{x_1, \dots, x_N\}$ from a $k$ component Gaussian Mixture model, with $k > 0$ known and is such that each \$x_i|\boldsymbol{\pi}, \boldsymbol{\mu} \sim \sum_{j=1}^{k}...
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### Gibbs sampler for Dirichlet Process concentration parameter

I am trying to implement a Gibbs sampler for Hierarchical Dirichlet process, but I cannot seem to correctly estimate the concentration parameters. I therefore started testing just this part of a ...
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### Conditional Distribution to sample

Suppose I have six data points (n,x): (14,5), (13,4), (7,3), (10,5), (12,7), (20,13) which are realizations of binomial experiments on n trials with x successes respectively.. And I assume I ...