# 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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### Calculating Metropolis-Hastings algorithm correction term

I am teaching myself about different samplers and currently going through a course. They write up an example of the Metropolis algorithm (MA), which I am pretty sure I understand. They next propose ...
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### Is the Jacobian term needed if the prior is on the transformation parameter?

Suppose I have a strictly positive parameter $\sigma$ and I need to estimate it using the random walk Metropolis-Hasting algorithm. I know that I can do a parameter transform, i.e., $\beta=log(\sigma)$...
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### Interpret and assess the output of MCMC in high dimension?

In one of my recent presentations I used MCMC to generate 50,000 samples from a 13-dimensional random variable. And the audience of this presentation is largely made up of layperson that has no ...
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### How can I find the acceptance probability for a joint Metropolis-Hastings proposal?

Suppose that I want to generate a proposal $(x^*,y^*,z^*)$ with the following: $$z^*\sim p(z|\alpha,\beta)$$ $$x^*\sim p(x|z^*,\boldsymbol{\gamma}_x)$$ $$y^*\sim p(y|z^*,\boldsymbol{\gamma}_y),$$ ...
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### Is this Categorical Distribution a valid proposal for Metropolis Hastings?

Is it possible to use a categorical distribution as proposal distribution for Metropolis-Hastings? For example, suppose that at the current iteration we are at the state $x_{i}=1$, from which there ...
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### How to understand the scaling in Metropolis Hastings MCMC

We know the Metropolis Hastings (MH) in MCMC: target distribution: $\pi(x)$ proposal distribution: $p(y|x)$ acceptance: $\alpha(x,y) = \min \Big(1, \dfrac{\pi(y)p(y|x)}{\pi(x)p(x|y)}\Big)$ Here are ...
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### Measure to capture within-chain fluctuations in MCMC?

I am using two kinds of updates for a particular parameter in MCMC estimation of my model. First update gives the following trace plot: Second update gives the following trace plot: Note that the ...
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