# 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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### Criteria in determining “step size” of Metropolis-hasting algorithms

I am training a complex Bayesian model using Gibbs sampling and Metropolis-Hasting algorithm. Most of the parameters are directly sampled by using conjugate priors except for 3 params which are ...
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### MCMC in a frequentist setting

I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM ...
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### What is the common criterion to decide the performance of prior selection in MCMC

For a model with likelihood $p(Y|\theta)$, in which $Y$ is the data and $\theta$ is the parameters. Based on Bayes Rule, we have the posterior $p(\theta|Y) \propto p(Y|\theta) p(\theta)$ My ...
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### How to solve MALA when the target density is known up to a constant?

If you look at the wikipedia explanation of Metropolis adjusted Langevin Algorithm, the acceptance ratio is given by The second equation involves taking the gradient of the log of $\pi(x)$. However, ...
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### Convergence of the Independent Metropolis-Hastings algorithm

I am interested in the convergence properties of the Metropolis-within-Gibbs sampler with Independent or Random walk. In this paper, I have read that in the case of an Independent walk, the proposal ...
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### RW Metropolis and ARMS fail

I've been trying to estimate a series of simulated Gamma-distributed random variables and its structural parameters with MCMC for a stochastic volatility model. However, both the random walk ...
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### Use of Metropolis & Rejection & Inverse Transform sampling methods

I know that the Inverse Transform method is not always a good option to sample from distributions because it is a analytical method dependent on the shape of the distribution function. For example, ...
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### Metropolis–Hastings algorithm variance isn't converging in R?

I'm trying to simulate a sample from a t distribution with 4 degrees of freedom. The candidate density I'm using is a normal(0,1) distribution. Although the mean does converge to 0, the variance keeps ...
1answer
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### Can adaptive MCMC be trusted?

I am reading about adaptive MCMC (see e.g., Chapter 4 of the Handbook of Markov Chain Monte Carlo, ed. Brooks et al., 2011; and also Andrieu & Thoms, 2008). The main result of Roberts and ...
1answer
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### MCMC how to choose standard deviation of sampling density

I'm using Metropolis-Hastings MCMC to find the set of parameters $\theta$ of a model $M$ that best fits my experimental data $x$ (with noise), where it is possible to directly calculate $x$ (without ...
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### MCMC with dependent variables

I want to run Metropolis-Hastings on a problem which involves two parameters that are not independent. I.e. I want to estimate both of these parameters. At the moment I'm trying to understand if this ...
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### Conditional Density for Sigma (Bayesian Lasso)

I found that in Bayesian Lasso commonly $\beta \sim N(0,\sigma^2*diag(\tau))$ and $\sigma,\tau \sim \pi(\sigma,\tau)$ is used. Whereas $\pi(\cdot)$ is a product of Laplace distributions. Is it ...
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### Narrow distribution and Hasting-Metropolis

I would like to sample from a density $\tilde{\pi}=C(\pi)\pi$ whose support is $[0,1]$. The normalization constant $C(\pi)$ of the function $\pi$ is unknown and $\pi$ is very narrow. To see how narrow ...
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### Is it possible for Metropolis sampling to converge to the wrong value?

I have simulated data under three parameters of interest, say a, b, c. The prior I put on c was a Gamma, so it only takes positive values. The full conditionals of a and b are known distributions, but ...
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### Metropolis sampling (symmetric proposal distribution)

Can Metropolis sampling be used in conjunction with Gibbs sampling? So for example, if I have three parameters of interest, but only two of them have full conditionals that are known distributions, ...
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### Likelihood overflow in Metropolis-Hastings acceptance probability

Consider a Bayesian framework where we have priors for some parameters and a likelihood based on the data. Consider the likelihood (and its parametric format) to be very sensitive to the choice of the ...
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### Sampling the scale parameter of a Laplace distribution

I need to adjust the scale parameter $\lambda$ of a Laplace prior ($p(x|\lambda)=(1/2\lambda)* exp(-|x|/\lambda)$) within metropolis hastings. That means I have a couple of draws for x and now I have ...
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### Sampling on a logarithmic scale

I have to draw samples (variance parameter) based on a Gaussian kernel but on a logarithmic scale. I have no clue how to implement that as a part of the Metropolis-Hastings algorithm. In particular, ...
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### Gibbs sampling with mixed prior using a Metropolis-Hastings step

My questions are about a sampling procedure for ﬁtting a Bayesian hierarchical model where one of the priors is a mixture distribution of discrete and continuous parts. The model is not my own but I ...