# 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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### 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 ...
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### Gibbs sampling for inferring the parameters of a GMM

I came across the following in Kevin Murphy's "a probabilistic perspective on machine learning". I am struggling to understand the derivation of the conditional probability for $z_i$. I tried ...
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### 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 ...
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### Gibbs Sampling for Gaussian Mixtures

Does the Gibbs sampler converge to a global maximum in the presence of multiple modes? For example in case of a Gaussian mixture distribution?
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### Sampling covariance matrix using Gibbs sampling

I am sampling covariance matrix from a Inverse Wishart distribution. In one dimensional case, after doing sufficient iterations I am taking the mode value for variance (after removing the burn-in ...
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### Multi-steps direct forecasting in AR(2) model through bayesian estimation of the model

I'm estimating an AR(2) model using Bayesian methods through Gibbs sampling and I want to perform 4 step ahead multi-steps direct forecasts. Inside the MCMC loop in each iteration I'm drawing the ...
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### Gibbs sampling example of a bivariate normal with unknown correlation

I'm looking for an example of using Gibbs sampling with a bivariate normal, where the correlation parameter is not fixed or known. In other words, what is the conditional distribution of the ...
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### Stationarity of coefficients when sampling VAR by Gibbs sampler

I am using Gibbs Sampler for VAR and have noticed that some researchers check the stationarity of $\beta$ coefficients while drawing. I am not sure why do they do that? Bayesian VARs do not require ...
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### What is the role of simulated annealing in Gibbs sampling?

While I was reading about Gibbs sampling, I happened to see "simulated annealing" but what is it doing in Gibbs sampling? Although I don't understand the full context of simulated annealing, I am ...
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### Does Gibbs sampling require to know the partition function?

As the title suggest, does gibbs sampling require to know the partition function? For example, if I want to sample variable $a$ and I have worked out $p(a|rest) \propto f(a|rest)$ where $rest$ ...
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### Influence of word counts from DTM on LDA with Gibbs Sampling

I'm trying to wrap my head around Topic Modeling based on LDA with Gibbs sampling (Griffiths, Steyvers 2004: Finding Scientific Topics). What struck me when reading some Python implementations like ...
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### Sampling from the joint distribution p(x,y) when y = f(x)

Suppose I want to sample from the joint distribution $p(X, Y)$, where $X$ is a random variable and $Y = f(X)$ where $f$ is a known function of $X$. However, sampling from $p(X,Y)$ directly is hard. ...
I have a question regarding section 7.1.1 here. I have two questions to ask you. What does the following sentence mean? we shall be drawing values for $C_T,C_{T-1},\cdots,C_1$ in order. How the ...