# 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).

102 questions
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### Is my OpenBUGS / WinBUGS model well specified?

I've just started trying to use OpenBUGS for Bayesian analysis of stochastic volatility models. In particular, I'm trying to calculate stochastic covariance, similar to the DC-MSV model specified by ...
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### full conditional posteriors for bayesian lasso

I am reading the original Bayesian Lasso paper, and its follow up; They look straightforward to implement, mainly because of the conditional posterior probability for the gibbs sampler; however, I ...
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### Conjugate prior for multivariate with known mean and covariance known to a constant

I have a linear trend model (evolving mean and slope) embedded in a larger state space time series model that I would like to constrain to be a spline. With that assumption, the mean and trend ...
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### Understanding a measure of convergence of MCMC simulations

I am trying to better understand better the Gelman/Rubin measure of convergence of MCMCs. The method starts off by defining two quantities: $B$ and $W$. $B$ is said to be the between chain variance (...
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### Practical Implementation of Gibbs Sampling in Latent Dirichlet Allocation

In the collapsed Gibbs sampling version of LDA, the posterior distribution of topic assignments for each word is sampled. From what I have read (e.g. http://people.cs.umass.edu/~wallach/courses/s11/...
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### Gibbs sampler for local linear trend model

Question: Consider the local linear trend model given by: \begin{align*} y_t = \mu_t + \tau \varepsilon_t \ \cdots \ \text{Observation equation} \\ \mu_{t+1} = \phi \mu_t + \eta_t \ \cdots \ \text{...
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### Sampling Stationary Vector Autoregression coefficients while Gibbs Sampling

I have been estimating a Bayesian Vector Autoregression using Gibbs Sampling. When constructing the posterior predictive distribution, I have noticed that when the simulated coefficients from the MCMC ...
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### Gibbs sampler on the precision (with a gamma prior) in a hierarchical Bayesian model doesn't converge

I am deriving a Gibbs sampler with a model similar to the model in this paper (a graphical model is shown in page 4). To put it simple, my question only concerns $w_i$ (a $K$-dimensional vector drawn ...
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### Finding the posterior distribution of mean and variance given data sample using Gibbs Sampling?

I have the following hierachical bayesian model - $\mathbf{x}|\mathbf{c},\sigma^2 \sim \mathcal{N}(\mathbf{x}|\mathbf{c},\sigma^2)$ \$\mathbf{c}|\mathbf{c}_1,\sigma^2_2 \sim \mathcal{N}(\mathbf{c}|\...
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### How exactly does Gibbs sampling work in Markov Networks?

I was going through the Probabilistic Graphical Modelling course by Stanford and they used a network such as this one-https://imgur.com/gallery/k0C8FY2 Now if we want to sample P(A|B), how would we ...
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### HDP: Gibbs sampler implementation

I am trying to recreate the model proposed by Gao et al. (2011), based on the Hierarchical Dirichlet Process proposed by Teh and al. (2005). To estimate the model (let's call it iHDP) I need to ...
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### Non-Identifiable Multivariate Normal Posterior

So I have a theoretical question about what looks like, in my opinion, a multivariate normal distribution. The issue comes with the fact that the data is distributed with likelihood: Y |θ1, θ2 ∼ N(θ1 ...
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### help interpreting plot of MCMC sample

I am estimating a model using MCMC (Gibbs Sampling). Because of the complexity of the model, I have been running two chains with many iterations. A plot of the draws for each parameter reveals a ...