Tagged Questions

7
votes
1answer
163 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 ...
1
vote
1answer
60 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
votes
0answers
90 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 ...
1
vote
0answers
53 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
vote
1answer
82 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 ...
3
votes
2answers
295 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 ...
3
votes
1answer
112 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 ...
2
votes
2answers
493 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
394 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 ...
3
votes
1answer
195 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
375 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
175 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
704 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.
3
votes
2answers
244 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 ...
10
votes
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 ...