# 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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### 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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### 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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### antagonistic simulated annealing

Simulated annealing aims at a series of target distributions $$\pi_T(x)\propto\exp\{T\,H(x)\}$$ to find the maximum of the function $H$ and its argument $$\arg_x\max_{x\in \mathfrak X} H(x)$$ if the ...
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### How to implement a M-H step in a Gibbs sampling

I am having trouble implementing a Metropolis Hastings step in a Gibbs sampling problem. The following code was taken from https://www.stat.colostate.edu/computationalstatistics/ Details: It is a ...
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### Gibbs Sampling vs. Using Raw Probability in Contrastive Divergence

In Hinton's Practical Guide to Training Restricted Boltzmann Machines, Section 3, he discusses different situations in which one should take a sample from the Gibbs sampling process, and other ...
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### Bayesian estimation of Dynamic Regression with AR(1) parameters

I would like to draw (Bayesian) inference in a dynamic linear regression with regression parameters following independent AR(1) processes $\beta_{t,i} = \mu_i+\beta_{t-1,i}+w_{t,i}$. However, I ...
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### When Gibbs Sampling is fast/slow to converge?

Are there any heuristic/theories showing that on what kind of Bayesian models the convergence of Gibbs sampling is fast/slow? For example, from my limited experience, I feel (may be wrong) when a ...
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### Efficiency in Metropolis Vs Gibbs sampling

I have read that Gibbs sampling is more efficient than Metropolis algorithm. Why? Is this due only to the fact the in Gibbs sampling the acceptance rate is $1$, so that the chain needs fewer ...
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I want to estimate the volatility $\sigma$ of a process $(X_t)$ following an arithmetic Brownian motion, that is, for a constant time step $\Delta$, $X_{t+\Delta} = X_t + \sigma B_{\Delta}$ , where $... 1answer 324 views ### What does it means of Normalization term of Gibbs distribution? I am studying about Gibbs distribution concept and I am confusing a one term in that concept that is normalization term. According to the Hammersley–Clifford theorem, an random$x$can equivalently be ... 0answers 94 views ### Can I use Adaptive MCMC in any setting? In time series econometrics and finance, most Bayesian authors approximate their models with a Gibbs Sampler, this is especial true for state space models, SV and so forth. The dimensionality of ... 0answers 253 views ### Gibbs sampling version for estimating Hierarchical Double Dirichlet Process Mixture of Gaussian Processes I'm trying to implement Gibbs sampling to estimate the parameters of the following non-parametric model:$\begin{align*} \beta|\gamma & \sim \text{GEM}(\gamma)\\ k_t|\beta & \sim \beta\\ \pi|\... 0answers 227 views ### 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 ... 0answers 152 views ### 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$is said to be the between chain variance (... 0answers 186 views ### Gibbs sample from AR(1) of exogenous input I am trying to fit a model where there is a sequence of exogenous "shocks",$X_1, X_2, ..., X_T$, and a AR(1) of these shocks explain$Y_1, Y_2, ..., Y_T$. Specifically, Data (known):$X_1, X_2, ...,...
I am trying to implement a mixture model of probits to infer the best decision boundary for every latent subpopulation. When doing Gibbs sampling, we eventually have to compute $P(y^* | w_c)$ where \$...