# 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).

372 questions
Filter by
Sorted by
Tagged with
0answers
16 views

1answer
220 views

### Gibbs Sampler for Normal and Inverse Gamma Distribution in R

I'm trying to implement a Gibbs sampler for the following conditional distributions using R: This is the code I have in R so far: ...
0answers
16 views

0answers
12 views

### Sampling Complexity for Gibbs sampling

I am trying to understand what is the sampling complexity of the best-known classical algorithm (along the lines of contrastive divergence etc) for drawing a sample from Gibbs distribution in terms of ...
0answers
13 views

### How to find conditional density?

Suppose there is a unit $\mathcal{l}_p$ ball $$B_p = \{ x \vert \sum^n_{i=1}\vert x_i \vert^p \le 1\},$$ where $p \ge 1$, $n$ is the dimension of the space and $x_i$ is the $i$-th coordinate of $x$. ...
0answers
15 views

### 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 $\theta_1, \theta_2$. ...
1answer
38 views

### 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 ...
1answer
39 views

### 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 ...
0answers
17 views

### 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?
0answers
12 views

### How to sample posterior distribution for models with random effects?

I have a time series model contains some fixed parameters ($\beta_{1}$, k, m, etc. ) and also a random effect (i.e. $\beta_{t}$ follows a random walk, with starting value $\beta_{1}$ and variance ...
1answer
127 views

### 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.
0answers
24 views

### 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 ...
0answers
28 views

### 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, ...
0answers
29 views

### 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 ...
0answers
18 views

### 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 ...
0answers
45 views

### 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 ...
1answer
88 views

### 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 ...
1answer
110 views

### 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 ...
2answers
289 views

### 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 ...
0answers
130 views

### 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 ...
0answers
61 views

### Intuition on why Gibbs Sampling samples from the posterior distribution

I am new to Gibbs Sampling and I do understand how the algorithm works but I would also like to understand how sampling from the conditional distributions is equivalent to sampling from the joint. ...
0answers
13 views

### Uncorrelated Samples from a non-conjugate (but well behaved) posterior

I'm trying to create a Dirichlet process mixture model with a kernel distribution similar to a product of gammas. (in fact, if I generate a latent random variable, it IS a product of (independent) ...
0answers
18 views

### How does pymc3 posterior simulation work in this simple case without having the full conditional distributions?

I'm trying to estimate the posterior distribution of the gamma parameters alpha and beta given that my data comes from a gamma distribution and the priors I chose come from two uniform distributions. ...
1answer
39 views

### Running several MCMC chains after convergence?

I am running a MCMC Gibbs sampler for a computationally expensive model. It takes ~12 hours to obtain 1000 iterations of this MCMC sampler. I have tested the sampler, and I found that the chain seems ...
0answers
41 views

### Estimating parameters with Gibbs sampling?

I've been trying to understand Gibbs sampling; my end goal is to intuitively understand it in the context of MCMC methods. However, in order to reach that end, I started a with simpler example. I ...
0answers
14 views

0answers
39 views

### Sampling states of an “unnatural” Hamiltonian System

I would like to sample from a Gibbs distribution given by $$f(p, q) = \frac{1}{\mathcal{Z}}e^{-H(p, q; \omega, J)}$$ where $H$ is the Hamiltonian on generalized coordinates \$(p,q)\in \mathbb{R}^{2n}...
0answers
22 views

### Why the nodes in a Boltzmann machine need to be sampled one at a time?

Typically, we use Gibbs sampling to update (or generate samples from) energy based models. This means we update each node while keeping its markov blanket constant. Why can't we update/sample all ...