Questions tagged [metropolis-hastings]

A special type of Markov Chain Monte Carlo (MCMC) algorithm used to simulate from complex probability distributions. It is validated by Markov chain theory and offers a wide range of possible implementations.

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Help to Proof of Gibbs sampler acceptance rate

i was wondering if someone could explain how the acceptance rate in the Gibbs Sampling works. In the literature it says that in Gibbs case, the acceptance is always 1 because part of the "...
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Bayesian analysis example with convergence under Gibbs but not Metropolis-Hastings

Having a conceptual understanding of algorithms such as Metropolis-Hastings, Gibbs and Hamiltonian Monte Carlo can provide ideas of remediation to apply when models do not converge. This question ...
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Metropolis Ergodicity

I have encountered one last problem with regarding to the Metropolis-Hastings algorithm. I know that ergodicity is needed in the algorithm to imply convergence to a unique stationary distribution. But ...
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In Bayesian models, can you use Uniform(-inf, inf) as a prior?

In Bayesian models, can you use Uniform(-inf, inf) as a prior? I ask because in an class, we looked at MH MCMC sampler, and showed that to sample from a distribution, we need not explicitly solve for ...
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Metropolis Hastings on hierarchical bayes update question:

[I have this somewhat complicated hierarchical bayesian model]1 Here the $y$ on $\theta$ are Poisson, $\theta$ are deterministically generated from the $att, def$ (and $home$). Then the last ...
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Optimal way to calculate the sample variance of MCMC data?

I assume that the calculation of the average and variance of a sample generated by a Metropolis-Hastings MCMC does not depend on the existence of correlation. Recently, I was told that in the presence ...
525 views

MCMC acceptance rate decreases when proposal variance gets smaller

I am drawing a sample Y of size n from a p-dimensional Normal ($\mu, \Sigma$). Typically, p is 5. I have $\bar{Y}$ and $V = YY'$, the sum of squares. Now I want to draw samples from this $\bar{Y}$, ...
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Application of Metropolis Hastings

I am trying to implement the Metropolis Hastings algorithm for Bayesian analysis. In this case, the parameter of interest is the scale parameter for a Weibull distribution. The context is for ...
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Computing the acceptance rate (empirically) of samples from the Metropolis algorithm, where samples are "thinned"

I have a number of queries about computing the acceptance rate of samples generated from the Metropolis (symmetric random walk) algorithm empirically, that is, in the presence of burning-in and ...
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Thinning and burn-in in Metropolis-Hastings algorithm

I have written a Metropolis-Hastings algorithm manually in Julia language for a customized distribution, and i want now to know how can i perform the thinning and the burn-in to increase the ...
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How do we define the kernel to calculate the acceptance ratio for Metropolis-Hastings Markov Chain Monte Carlo?

I am having a lot of difficulty understanding how to apply the algorithm to a real scenario. The part that confuses me is that we are looking for a target distribution (the real distribution of our ...
102 views

Metropolis-Hastings with non-centered Proposal

I am trying to draw samples from the Laplace distribution $\pi^* = \text{exp}(-|\theta|)$, using Metropolis Hastings algorithm with a noncentered proposal, meaning that regular Metropolis wont work.. ...