Tagged Questions

2
votes
1answer
88 views

Most efficient way of sampling a product of distributions $k \cdot f(x) \cdot g(x)$, given that PDFs $f(x)$ and $g(x)$ can easily sampled?

Is there an efficient approach tailored to sampling from a PDF $k \cdot f(x) \cdot g(x)$ (where $k$ is a normalizing constant) that would perform better than naive Metropolis, slice sampling, etc.? ...
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
97 views

Generation of a random vector on an affine hyperplane

I would like to design a proposal of the form: $$ p(t=(t_i)|\hat{t}=(\hat{t}_i)) $$ where $t$ (and $\hat{t}$) lies in an affine hyperplane $T \subset R^n$: $$ t \in T \Leftrightarrow \sum_i t_i=1 ...
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
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
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 ...
1
vote
1answer
54 views

When is blocked Metropolis sampling more efficient?

Consider the problem of sampling from $p(\mathbf{x}, \mathbf{y})$ using the Metropolis or Metropolis-Hastings (MH) algorithm. I can either propose samples for $p(\mathbf{x}, \mathbf{y})$ directly, or ...
2
votes
1answer
142 views

Sampling in discrete distribution

At the moment I'm working with an algorithm that calculates probabilities $Z$ for a finite sequence of data points $X= \left\{ x_1,x_2,...,x_n \right\}$ using an expression like: $p(Z_i| X_i,\theta) = ...
2
votes
0answers
33 views

Sampling from elliptic pde solution in high dimensions

What is known about sampling from solutions to elliptic PDE's in high dimensions, where it is computationally infeasible to construct or store the actual solution? For example, let $u$ solve the ...
1
vote
0answers
78 views

Is the following a valid MCMC sampler?

I have a model with two variables $X_1$ and $X_2$. In general, I would like to create a Gibbs sampler based on the conditionals $p(X_1 | X_2)$ and $p(X_2 | X_1)$. However, computing either $p(X_2 | ...
2
votes
2answers
494 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
397 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 ...
4
votes
1answer
189 views

Can one alter a MCMC method to reduce variance when the function of interest (not just the distribution) is complex?

Consider approximating the following expectation: $$\mathbb{E}[h(x)] = \int h(x)\pi(x) dx$$ Where $h(x)$ is an arbitrary function and $\pi(x)$ is a distribution for which the normalizing constant is ...
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 ...
4
votes
1answer
392 views

Sequential Monte Carlo (particle filter) with Metropolis-Hastings weighting

Let's say we are interested in approximating the following expectation: $$\mathbb{E}[h(x)] = \int h(x)\pi(x) dx$$ Where $h(x)$ is an arbitrary function and $\pi(x)$ is a distribution known only up ...
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.
0
votes
1answer
230 views

Reusing past MCMC samples from a similar distribution

I have two graphical models that have significant overlap in the random variables they are modeling. Is it possible to use samples from one graphical model to avoid sampling as much from the other ...
3
votes
2answers
245 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 ...
2
votes
2answers
199 views

What is the most computationally efficient way to sample from an unnormalized density?

EDIT: After doing some more research, it seems slice sampling could be the way to go. I've seen it mentioned a lot in the context of how to sample the univariate distributions required for Gibbs ...
6
votes
2answers
553 views

Acceptance rates for Metropolis-Hastings with uniform candidate distribution

When running the Metropolis-Hastings algorithm with uniform candidate distributions, what is the rationale of having acceptance rates around 20%? My thinking is: once the true (or close to true) ...
5
votes
1answer
222 views

Modeling multinomial problems with unknown sample size in BUGS

I'm trying to estimate the design effect of a series of relatively small sample size surveys ($n\sim 70$) with multiple responses. Design effects roughly correspond to how much larger actual sample ...
2
votes
1answer
257 views

Nonparametric expected value estimation of sample from unknown distribution

I have a data sample (in this case an EEG data sample, but my question refers to any type of data samples of prior unknown distributions). I would like to do a nonparametric estimate of the expected ...
7
votes
2answers
498 views

Using MCMC to evaluate the expected value of a high-dimensional function

I am working on a research project that is related to optimization and recently had an idea to use MCMC in this setting. Unfortunately, I am fairly new to MCMC methods so I had several questions. I'll ...