# 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).

417 questions
Filter by
Sorted by
Tagged with
5 views

• 45
1 vote
114 views

• 123
256 views

### Distribution of conditional posterior for Gibbs sampling

The following is a description of how the authors (Yongning Wang & Ruey S. Tsay) of this (2019) paper Clustering Multiple Time Series with Structural Breaks want to perform Gibbs sampling to ...
1 vote
151 views

### Mean of skew normal distribution with normal prior obtained with Gibbs sampling

I would like to obtain a new mean $\mu$ of a skew normal distribution with a normal prior of the form $N(\delta,\tau)$ on $\mu$, and a given standard deviation $\sigma$ and shape parameter $\alpha$. ...
• 11
346 views

### Bayesian updates for Dirichlet-multinomial with Gamma prior

Let \begin{aligned} X_i &\sim \text{Dir-multinom}(X\mid\lambda)\\ \lambda_{j} &\sim \text{Gamma}(\lambda_j\mid\alpha,\beta)\\ \end{aligned} where $i$ iterates over observations, $j$ ...
• 225
47 views

### Recovering samples from a density estimation with an additional prior on the samples. Used for Gibbs sampling

Abstract Idea: Given a noisy measured density ($d_j$ at position $p_j$) and a density model, sample from the model parameters under the following stochastic model: Stochastic Model: Prior for model ...
• 21
204 views

### Hyperprior in Gibbs Sampling

Following up from this question, I have managed to derive the following posterior distributions  \lambda_z | \boldsymbol{y}, \Theta^{(-\lambda_z)} \sim Gamma(a + \sum_{i=1}^{n_z} y_{ij}, \quad a + ...
• 11
1 vote
725 views

### Poisson-Gamma Hierarchical Model

I am fairly new to Gibbs Sampling and I am trying to build a Gibbs Sampler for a Poisson-Gamma hierarchical model. In this model, there are $m$ restaurants in a city, with $n_z$ number of observations ...
• 11
123 views

### Question about paper on Bayesian Shrinkage Estimation

I am reading the paper Bayesian Shrinkage Estimation of the Relative Abundance of mRNA Transcripts Using SAGE, and I am trying to work out the calculations for the complete conditionals for the Gibbs ...
828 views

### Gibbs Sampling - why converge to stationary distribution

Currently, I am going through Chapter 12.3 of Probabilistic Graphical Models - Principles and Techniques which talks about MCMC sampling methods. In Chapter 12.3.4.1, it states the following theorem: ...
• 31
1 vote