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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Sampling from conditional posterior - continuous and discrete terms

I'm working through Hierarchically Supervised LDA by Perotte et all (2011). The conditional posterior I'm supposed to sample values $z_i$ from, however, is zero almost everywhere. To see why, lets ...
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OpenBugs vs. JAGS

I am about to try out a BUGS style environment for estimating Bayesian models. Are there any important advantages to consider in choosing between OpenBugs or JAGS? Is one likely to replace the other ...
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Gibbs sampling with expectations instead of sampling

I see there is something called Iterated Conditional Models (ICM), which is a sort of Gibbs sampling where, instead of sampling, we use the value that maximizes the conditional. That is: ...
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Blocked Gibbs Sampling using Forward / Backward Algorithm

I am new to machine learning and have been reading about gibbs sampling. From my understanding, a Gibbs algorithm samples a single variable iteratively conditioned on all other variables. In blocked ...
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Unsupervised Bayesian naive Bayes

I'm reading a paper Gibbs sampling for the uninitiated. In this paper, the authors try to use Gibbs sampling for a bayesian naive bayes model. They formalize the model as a graphical model in page 8. ...
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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. ...
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Gibbs sampling on the use of gamma distribution

I am trying to reproduce a Gibbs sampling but some points are unclear to me. Let's assume a linear model of the following form $$y=x\beta + \epsilon$$ The prior distribution for the beta ...
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How does Gibbs sampling produce values for a variable using the univariate conditional probability?

I have a question about Gibbs sampling for generating samples. The Gibbs sampling algorithm is often stated. $x^0 = (x_1^0, x_2^0, \ldots, x_n^0)$ //initialize random values for $t=1$ in $T$ //...
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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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throwing away all Gibbs samples after approximation

This is more of a theory question, consider: $$P(w_1|D)=\int P(w_1|S)P(S|D)d(S)$$ which we approximate via Gibbs sampling $S$ (assume the initial state of the Gibbs sampler is denoted by $M_0$), ...
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handling metropolis hastings rejection during a Gibbs sweep

Suppose I have a MCMC involving a 2 step Gibbs sampler. The first part uses metropolis hastings to find the next parameter value. If during one sweep, the result for the first part is a rejections, ...
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A verifiable and teachable Gibbs example

I am attempting to construct a teachable example of Gibbs sampling that I can also relate to how it might be used on an actual dataset and yet could also be verified analytically by students with ...
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Methods to solve a compound distribution MLE I can't write in closed form

What are some methods of solving a MLE parameter estimate where the likelihood function can't be written in closed form? I have a compound distribution that I don't have a closed form for (no ...
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How to do MC integration from gibbs sampling of posterior

I'm a beginner of MCMC. Two questions confused me. If I know the posterior distribution, and from the Gibbs sampling, I got the sampled parameter, so How to draw the histogram with y axis as ...
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Generating Sample Path of HMM via Gibbs Sampling

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 ...
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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 ...
I'm trying to understand how to condition a probabilistic posterior distribution. Consider the following probability density:  p(\alpha, \beta | y) = \prod_{i=1}^n (\alpha+\beta t_i)^{y_i}e^{-(\...