# 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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### Binned resampling of correlated data with bootstrap method

The goal Compute the Binder cumulant defined as the estimator $$\text{B.C.}=\frac{\langle x^4\rangle}{\langle x^2\rangle^2}$$ and its statistical error on a sample of normally distributed data points ...
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### Why do we sample from the uniform distribution in Metropolis-Hastings for acceptance?

For each iteration of the MH, sample $x'=q(x|x')$, then the acceptance probability is computed:$$A=\min(1,a)$$ where $$\alpha=\frac{p(x')q(x|x')}{p(x)q(x'|x)}$$ Now, I've seen that the algorithm ...
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### Slice sampling in Particle Gibbs with Ancestral Sampling

Bear with me as I am not from statistical background. My question is about the implementation of PGAS algorithm as given in Lindsten et. al 2014 concerning sampling in state-space models. The two ...
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### Sampling for multimodal posterior using Metropolis-Hastings

I was wondering how the well-known Metropolis-Hastings algorithm changes when sampling from a multi-modal posterior. In particular I was wondering what would change in the acceptance ratio in order to ...
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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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### Drift and Minorization for Metropolis Hastings algorithm

Can some one point me to articles or literature with an example of the drift and minorization condition proof. At the moment i have come across the Gibbs Sampler and the Random Walk Metropolis ...
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### Question about MCMC independent proposals

I've a question re MCMC proposals, I was hoping you could help me with that. I need to implement for work an Independent Metropolis-Hastings algorithm to sample from a 10-dimensional posterior. I am ...
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### Best Proposal Distribution for asymmetric target in Metropolis Hastings (Exponential Target)

Suppose I know my target distribution is asymmetric, for instance, suppose my target distribution is an exponential $$p(x) = e^{-x} \qquad\qquad x\in [0, +\infty)$$ Is there any theory regarding ...