The gibbs tag has no wiki summary.
0
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1answer
28 views
Looking for step by step example of sampling from DAG in Bayesian model
I am looking for a tutorial type example that shows the step by step process sampling from a simple hierarchical model.
For example, I am trying to study the distribution of ...
1
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2answers
176 views
PyMC: how can I define a function of two stochastic variables, with no closed-form distribution?
I'm learning PyMC and basically I have a random variable $Z = X + Y$ where (say) $X \sim \mathrm{Normal}(\theta_X)$ and $Y \sim \mathrm{Lognormal}(\theta_Y)$ and $Z$ has no simple closed-form ...
7
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1answer
167 views
Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (such as $k \cdot f(e^y)$)?
Say I'm able to sample an RV $X$ from a PDF $f(x)$, can I exploit this to efficiently sample another RV $Y \sim k \cdot f(g(y))$ (where $k$ is a normalizing constant)?
I'm interested in something ...
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0answers
30 views
Gibbs sampling product of normals as conditional
I am deriving a gibbs sampler for a joint distribution, where the conditionals of various parameters are product of two non-standard normal distributions. Usually, I have seen that in Gibbs sampling ...
1
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1answer
73 views
Sampling from conditional distribution in general case
I'm dealing with Gibbs Sampling now.
Let's consider the example:
I know the distribution of X|Y and the distribution
of Y. They are some known - Binomial or Beta or other
but particular. Thus I have ...
2
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1answer
76 views
Calculating conditional probability
I've got the next question.
Let's consider I have the pair of distributions:
X|t ~ Binomial(n,t); t~Beta(a,b). Here n,a,b are known.
I need to construct conditional probability to sample from it, t|X.
...
1
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1answer
65 views
Derivation of the posterior over topics in LDA
When studying the latent Dirichlet allocation, I am not very clear about some procedures in their deriving equations. Please refer to the attached figure, how to understand those two steps, marked as ...
2
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0answers
94 views
Gibbs sampling from full conditionals
I have the following joint density:
$p(x_1,x_2,y_1,y_2) \propto \exp\left(−\left(x_1^2+x_2^2+c_1(y_2-y_1)^2+c_2(y_2-y_1)^4\right)\right)$
Can I use Gibbs sampling to sample from that? How can I get ...
3
votes
2answers
190 views
Bayesian estimation of Dirichlet distribution parameters
I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that:
Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
0
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0answers
27 views
Gibbs Sampling weight more recent samples heavier?
I'm implementing an online Albert and Chib Gibbs sampler for Probit regression (see http://www.cs.ubc.ca/~emtiyaz/Writings/EMTstatisticalcomputation.pdf or ...
1
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0answers
54 views
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 ...
1
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1answer
87 views
Computing conditional expectation of ordered normal random variables
There are $m$ normally distributed, independent random variables $N_1, \ldots, N_m$ with distinct means $\mu_1, \ldots \mu_m$ and standard deviations $\sigma_1, \ldots, \sigma_m$. Then, we observe a ...
8
votes
1answer
245 views
What are some well known improvements over textbook MCMC algorithms that people use for bayesian inference?
When I'm coding a Monte Carlo simulation for some problem, and the model is simple enough, I use a very basic textbook Gibbs sampling. When it's not possible to use Gibbs sampling, I code the textbook ...
3
votes
2answers
344 views
Generating samples from gibbs sampling
I am quite new to sampling. I am doing Gibbs sampling for a Bayesian network. I am aware about the algorithm for the Gibbs sampling but one thing I am not able to understand.
For example let's ...
2
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0answers
130 views
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 ...
0
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1answer
151 views
Preparing Bayesian conditional distributions for Gibbs sampling
I was looking at the Gibbs Sampler when I stumbled upon the following example:
Suppose $y = (y_{1}, y_{2}, \ldots, y_{n})$ are iid observations from an $N(\mu, \tau^{-1})$
Furthermore, suppose there ...
3
votes
1answer
116 views
What is the state-of-the-art regarding sampling from discrete distribution?
After struggling with auto-Poisson model (a.k.a. Random Markov Network with conditional Poisson distributions) trying to force Gibbs sampler to obtain discrete sample of the network (since I know ...
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0answers
106 views
Test for convergence within Gibbs sampler
I am running a Gibbs sampler for Multivariate Normal times Inverse Wishart posterior distribution with missing data imputation step.
I am trying to check if my step of simulating covariance matrices ...
1
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0answers
179 views
Bayesian estimation using Gibbs sampling for financial models
I am trying to do Gibbs sampling, from this paper,
www.jds-online.com/file_download/353/JDS-746.pdf
This is a CIR financial model, I want to do Gibbs on its parameters:
...
1
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2answers
418 views
How to reduce autocorrelation in Metropolis algorithm?
I've been using a Metropolis/Gibbs sampler combination to generate a joint density for some parameters(it is a hierarchical model, with $y_i\sim Poisson(\lambda_i)$, $\lambda_i\sim ...
1
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0answers
98 views
MCMC algorithm to estimate beta and variance
I'm looking for a generic MCMC algorithm for a linear model. I've been reading a lot of articles online and they are so confusing.
I am hoping to understand how the method works theoretically
Can ...
2
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1answer
262 views
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?
2
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1answer
199 views
Non-conjugate improper uniform priors in Bayesian data analysis: how to handle infinite sums?
I've been working on Griddy Gibbs sampler (paper: Ritter and Tanner) and I've implemented it in R. But I've faced a problem when I started thinking on its uses in other contexts.
If I try to use an ...
2
votes
2answers
511 views
Gibbs sampler from conditional distribution
I am trying to propose Gibbs sampling with the density below,
$$p(y_1,y_2,y_3)\propto \exp [-({{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{\theta}_{12}{y_1}{y_2}}+{{\theta }_{13}{y_3}{y_1}}+{{\theta ...
1
vote
1answer
412 views
Need help on Gibbs sampling with truncated normal and gamma
I am trying to use Gibbs Sampling to simulate a random sample from a joint distribution $f(\beta ,{{Z}_{1}},...,{{Z}_{75}},{{\lambda }_{1}},...,{{\lambda }_{75}})$, where the fully conditioned ...
2
votes
1answer
572 views
Gibbs sampling from posterior distribution using R
New to MCMC.
I have a model, saying
$$Y_i=\beta_0+\beta_1x_{i1}+\beta_2x_{i2}+\frac{e_i}{\sqrt{\mu}}$$
where $x_{ij}$ are fixed covariates, $e_i\sim N(0,1)$, $\beta_0$, $\beta_1$, $\beta_2$ and $\mu$ ...
3
votes
1answer
200 views
Convergence results for block-gibbs sampling?
Suppose you have some complex model you want to sample from by Markov chain Monte Carlo. There are many types of situations where you can divide your variables into, say, two groups, and efficiently ...
3
votes
2answers
391 views
Sampling variables and calculating likelihood in WinBUGS/OpenBUGS
I am trying to read some WinBUGS/OpenBUGS examples to figure out how to specify models. I can't seem to understand where the probabilistic dnorm, ...
3
votes
1answer
177 views
Prior of multivariate Polya distribution?
Anyone knows a prior (preferably conjugate) to the
multivariate Polya distribution?
I need it for Gibbs sampling. So if anyone has another idea, I am interested.
2
votes
2answers
725 views
A robust R package to do MCMC and Gibbs sampling
I need to make linear model for which I need to do Gibbs sampling in MCMC simulations. The model needed to be fitted is a linear mixed model.
Please suggest me for a robust R package for this task.
1
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1answer
204 views
Drawing from a conditional density
I have a simple question. Suppose $X=(X_1,X_2,X_3)$ is multivariate normal. What's the best (quickest) way to draw from the conditional density $X_1\mid \exp(X_1)+\exp(X_2)+X_3$?
3
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2answers
250 views
Is sequential Bayesian updating an option when using MCMC?
I have an implementation of the Griddy Gibbs sampler, but my observations on which I'm conditioning model parameters are too many in number, thus the likelihood underflows quickly, even with a log ...
1
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0answers
90 views
Mathematical reference for the convergence in distribution of the Gibbs sampler
This question is in some sense the intersection of this question and this question. I have read up on the Gibbs sampler, and am now asking for an introduction to the Gibbs sampler for mathematicians. ...
10
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1answer
2k views
Can someone explain Gibbs sampling in very simple words?
I'm doing some reading on topic modeling (with Latent Dirichlet Allocation) which makes use of Gibbs sampling. As a newbie in statistics -- well, I know things like binomials, multinomials, priors etc ...
23
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4answers
981 views
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 ...
2
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2answers
213 views
Resources about Gibbs sampling in hybrid Bayesian networks
Greetings,
I've been trying to get my hands on a substantial resource for using Gibbs sampling in hybrid Bayesian networks, that is, networks with both continuous and discrete variables.
So far I ...
13
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3answers
1k views
A good Gibbs sampling tutorials and references
I want to learn how Gibbs Sampling works and I am looking for a good basic to intermediate paper. I have a computer science background and basic statistic knowledge.
Anyone has read good material ...
1
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1answer
674 views
JAGS: posterior predictive distribution
I am fitting a simple linear regression model with R & JAGS:
...
1
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2answers
449 views
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 ...
1
vote
1answer
345 views
Posterior expression for Gibbs sampling
I am trying to estimate parameters of a two dimensional Normal distribution using Gibbs sampling. While it was very easy transform the posterior equation for mean vector to a single dimension normal ...
1
vote
1answer
413 views
Comparison of Slice sampling and Gibbs sampling
To me, the two are similar in the sense that slice sampling is just Gibbs sampling for the uniform distribution over the area under the plot of the density function. Is that right?
I was wondering if ...
7
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2answers
2k views
Gibbs sampling— where do the full conditionals come from?
So MCMC algorithms like metropolis hastings and gibbs sampling are ways of sampling from the joint posterior distributions.
I think I understand and can implement metropolis-hasting pretty easily-- ...
