# 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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### slice sampling within a Gibbs sampler

Questions My questions are: Is the following slice-sampling-within-Gibbs approach valid? Is there a good reference out there that uses, or better yet, justifies it? Context I'm trying to sample ...
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### Clustering methods for unknown number of clusters

Matrix $X=[x_1,...,x_i,...,x_N]$ is a data-set containing $N$ data-points that each data-point $x_i$ is a vector of $D$ dimensions. Each dimension is a feature. The number of clusters ($K$) is unknown....
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### How to use Gibbs sampling when target function is known only up to normalising constant?

Assume we want to use Gibbs sampling to get an estimate of the parameter , and that we have the following expression for the conditional posterior of : If I am not mistaken, this means that the ...
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### Methods of fitting a dynamic linear model

I'm taking a time series course and am learning about exchangeable time series form of dynamic linear models (DLMs). This is given by: \begin{align*} \mathbf{y}_t' &= \mathbf{F}_t'\boldsymbol{\...
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### What are the main differences between classical and Gibbs sampling Latent Dirichlet Allocations?

In these weeks I have been studying the classical Latent Dirichlet Allocation (LDA) algorithm by David Blei and colleagues (2003), and the LDA variant based on Gibbs sampling introduced by Tom ...
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### Estimation of Bayesian Models

I'm trying to get into Bayesian model estimation (I'm interested in posterior parameter distributions). I could get away with Metropolis-Hastings and Gibbs Sampling for models with few parameters (<...
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### Gibbs sampling deriving complete conditionals with mixture priors

My question is about the derivation of the complete conditionals for Gibbs sampling in a hierarchical model where some of the parameters are mixtures of point-masses and Normal distributions. The ...
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### Canonical example to understand Gibbs Sampling

I'm been trying to understand Gibbs sampling. What I'm looking for is a paper or other reference which uses a simple canonical example and uses that to illustrate Gibbs sampling. Sadly I've not ...
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