# 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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### 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 $\alpha$. ...
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### Posterior predictive distribution of Gibbs Sampling compared to original data

I have implemented a Gibbs sampler to simulate from the joint posterior: $ln(y_1),...,ln(y_n)|\mu,\sigma^2 ∼_{iid} N(\mu,\sigma^2)$ Where both $\mu$ and $\sigma^2$ was unknown. I have simulated values ...
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### 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, $j$ ...
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### 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 ...
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### Differenciate between two distributions using gibbs sampling [closed]

This question is relate to the post : " Conditional distribution for Gibbs sampling for Gaussian mixture " but is a little bit different. My objective is to know why the algorithm (which is ...
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### Measure to capture within-chain fluctuations in MCMC?

I am using two kinds of updates for a particular parameter in MCMC estimation of my model. First update gives the following trace plot: Second update gives the following trace plot: Note that the ...
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### MCMC algorithm for Hierarchical Bayes model with variable number of mixture components

I am trying to develop an MCMC algorithm for clustering $n$ data-points $y_{1},y_{2},\dots,y_{n}$ using a Gaussian mixture model, but with a prior defined on the number of components K. The ...
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### Gibbs sampling step for variables that have a complex offline prior in an MCMC hybrid

I have a question about how to use an offline function as a prior when performing a Gibbs/hybrid analysis. Let's say I have data $y$ and some parameters which I'll simplify to $\theta_1, \theta_2$. ...
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### Expanding conditional probability for Gibbs sampling with many parameters

I'm trying to use Gibbs sampling to get the following target distribution: $$p(a,b,c \lvert x, z)$$ Where $z = f(x,a,b,c)$ and the rest are independent. I know the following conditional ...
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### Why iterations of Gibbs sampling for a bivariate Gaussian distribution can be seen as random walk?

In Section 4.4 of the excellent technical report Probabilistic Inference using Markov Chain Monte Carlo Methods, the author tries to analyze the performance of Gibbs and Metropolis algorithm with ...
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### Plotting a random walk on R [closed]

I've run a Gibbs sampler and obtained a sample for $X_1$ and $X_2$. I'm trying to recreate a plot like this one: How do I recreate the walk part on R?
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### How to built Gibbs sampler of Mixture Bayesian regression in R?

I am working on a Gibbs sampler of three parameters and we know the full conditional distribution of three parameters.
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### Particle Gibbs Sampler For Regime-Switching Nonlinear Gaussian SSM

I'm reading this paper on using a non-linear Gaussian SSM for measuring regime-switching leverage effect using stock market data. I'm using it as jump-off point for an undergraduate paper. My advisor ...
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### Gibbs updating algorithm (Gibbs steps) for computationally expensive likelihood

I am looking for a good way to update steps in a Gibbs sampler where the likelihood function is computationally expensive. Here is what I tried so far: By default JAGS uses a slice sampler. However, ...
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### Deriving a full conditional distribution when Half-t distribution is used

I'm trying to use a Half-t distribution with Gibbs sampling to form a model. but having hard time finding the full conditional distribution. Suppose $$Y = X \beta + \epsilon$$, where $Y$ is a ...
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### Gibbs sampling Bayesian conditional distribution for mean of a Normal distribution

first post here in CV. I'm currently working on a textbook exercise on Gibbs Sampling and got stuck on naming the distribution for one of the conditional distributions. Question Consider a normal ...
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### Gibbs sampler of a generative model

I understand what a Gibbs sampler is and I understand how LDA does classification. But I'm unsure how I can generate a Gibbs sampler for an LDA model and how to meld the two concepts. Let's say I ...
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### Bayesian mixture model joint posterior

I am just starting to learn about bayesian mixture models. There is a few clarifications that I want to make which I am not sure myself. The graphical model below describes a gaussian mixture model ...
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### Implementation of a blocked Gibbs sampler for a mixture model with a Dirichlet-process prior

I am trying to understand and implement the blocked Gibbs sampler described on page 552 in Bayesian Data Analysis by Gelman et al. in the context of using a Dirichlet process as a prior in a mixture ...
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### Deriving full conditionals from joint distributions?

In this link (https://www.youtube.com/watch?v=a_08GKWHFWo), the author derives the conditional distributions from the joint; but I got lost in the mechanics of what happened, the process was overly ...
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### Gibbs sampling proposals for bivariate normal?

I'm very familiar with Metropolis-Hastings, having implemented the algorithm myself to handle "toy problems." Gibbs sampling, however, is a bit trickier for me as I'm not quite certain what ...
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