-1
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0answers
7 views

Paper about Curse of Dimensionality of Gibbs Sampling

Do you know some references from the literature providing details about the curse of dimensionality of Gibbs sampling? Thanks!
0
votes
0answers
14 views

Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications. Using the Metropolis-Hastings scheme to accept/reject the proposed models is smth that i thought i completely understood, but i don't. To be ...
1
vote
1answer
67 views

Proving that Markov Chain Monte Carlo converges

I am trying to understand how the very basic Markov Chain Monte Carlo approach works: We try to approximately calculate the expected value $E_{\pi(x)}[X]$ by drawing sequential samples from a Markov ...
1
vote
1answer
90 views

Why Gibbs sampling needn't “remixing”

I am generating $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)}$ using Gibbs sampling methods. So I want $\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, \dots, \mathbf{x}^{(n)} \sim$ some ...
0
votes
1answer
121 views

Markov Chain Monte Carlo in plain English

I barely know what a markov chain is (I had a terrible teacher) and I probably have an idea of what a stationary distribution is... but I don't know how a Monte Carlo method works and I don't know how ...
1
vote
0answers
49 views

Gibbs / MCMC sampling for sum of parameters - how to improve slow mixing?

Suppose I have a hierarchical Bayesian model, where my observational prediction, $y'$, is calculated as the sum of other parameters, ${\alpha_i}$. My observation equation (the likelihood) is: $P(y | ...
0
votes
1answer
96 views

Metropolis Hastings definition - Proving $\pi(x)$ is the invariant density of our transition matrix

I'm currently working through the proof of the Metropolis-Hastings algorithm, and using two sources: page 328, section 3 page 1704-1705 I have a good understanding of most of the proof until ...
2
votes
1answer
705 views

Acceptance probability of Metropolis-Hastings

I am an IT guy writing my masters thesis on MCMC methods for use in predicting the outcome of football(soccer) matches. Right now I am trying to wrap my head around MCMC and Metropolis-Hastings in ...
0
votes
1answer
35 views

Why cannot the Markov Chains used in MCMC simulations be null recurrent?

I am aware this question borderlines retardedness, but I am seeking an accurate explanation. I understand in null-recurrent cases, the expected amount of time to explore states can be infinite. Is ...
1
vote
0answers
45 views

How to sample the walk which visits each vertex of a graph specific number of times?

Is there any MCMC mathod that allow me to uniformly sample from all feasible walks where the following restrictions apply: ...
3
votes
3answers
188 views

Markov chain stationary probability simulation

Having a defined markov chain with a known transition matrix, rather than to calculate the steady state probabilities, I would like to simulate and estimate them. Firstly, from my understanding there ...
1
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0answers
161 views

Markov Chains - Using Gibbs & Metropolis algorithm.

Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate $(x_1,y_1), ...
2
votes
2answers
271 views

What does it mean for MCMC to converge?

I know that a Markov Chain is a discrete random process where the current state decides the next and in a random walk, the probability that we move from node u to v is 1/N(u). An MCMC sample will ...
1
vote
0answers
38 views

Integrating with respect to an MCMC Kernel

I'm currently trying to evaluate an integral with respect to an MCMC kernel, and I wanted someone else to read what I `proved' to see if it's really correct. It just doesn't feel right. Suppose I ...
2
votes
1answer
936 views

Computing the similarity between two matrices / Monte Carlo analysis

I am studying the article at the following link, http://www-stat.stanford.edu/~cgates/PERSI/papers/MCMCRev.pdf Which applies Monte Carlo analysis to a decryption problem. The math is admittedly over ...