Questions tagged [mcmc-acceptance-rate]

The acceptance rate (acceptance ratio, acceptance fraction) for a Markov Chain Monte Carlo sampler indicates the fraction of accepted over proposed moves.

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Need to understand a statement for Random Walk Metropolis algorithm's proposal distribution?

I was told that the proposal distribution of Random Walk Metropolis needs to be symmetric. But today I was reading a book about Bayesian Analysis which contains the following statement: "The proposal ...
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1answer
113 views

How to tune MCMC with unwieldy posterior [duplicate]

Let's say I have $n$ observations of a random variable, $X_1, \dotsm, X_n \sim \mathcal{N}(0, \sigma^2)$. I also assume $\sigma^2$ has a Gamma(1,1) prior distribution, $\pi(x) = \exp(-x)$. I'm now ...
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Hamiltonian Monte Carlo with acceptance threshold of zero

I realize this is an open-ended question, but I'll accept any answer with gives a reasonable explanation and something to try. I'm running Hamiltonian Monte Carlo, specially pyhmc, and logging the ...
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0answers
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Adaptive MCMC when variables exist only conditionally?

I'm looking at models that make the existence of one variable depend on another variable. For example, n ~ geometric(0.5) x ~ iid(n,normal(0,1)) Here, ...
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0answers
20 views

convergence and efficiency of mcmc chains and estimation of covariance matrix

I am doing some bayesian analysis and exploring posterior distribution with mcmc method. I would like some clarification with estimating the covariance matrix. I have a model with 6 parameters. ...
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37 views

Express the mean acceptance rate of the Metropolis-Hastings algorithm as a total variation distance

Let $(E,\mathcal E,\lambda)$ be a measure space $p:E\to[0,\infty)$ be $\mathcal E$-measurable with $$c:=\int p\:{\rm d}\lambda\in(0,\infty)$$ and $$\mu:=\underbrace{\frac1cp}_{=:\:\tilde p}\lambda$$ $...
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0answers
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Express the mean acceptance ratio of the Metropolis-Hastings algorithm as a total variation distance

Short question in Theorem 1 on page 3 here https://openreview.net/pdf?id=Hkg313AcFX, he mean acceptance ratio is expressed in terms of a total variation distance. However, I don't understand the ...
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1answer
161 views

Expression for the mean acceptance rate of the Metropolis-Hastings algorithm

Let $(E,\mathcal E,\lambda)$ be a measure space $p:E\to[0,\infty)$ be $\mathcal E$-measurable with $$c:=\int p\:{\rm d}\lambda\in(0,\infty)$$ and $$\mu:=\underbrace{\frac1cp}_{=:\:\tilde p}\lambda$$ $...
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0answers
72 views

MCMC Metropolis-Hastings sampler - Estimation of multiple parameters

First time that I ask a question on this platform! Here I go... I have a dataset with two random variables X1 and X2 and an output Y which comes from a discrete Weibull distribution. I've been trying ...
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0answers
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How to evaluate the draw from the proposal of a Metropolis-Hastings?

In the Metropolis-Hastings step of a MCMC, given a $\theta_n$, I'm drawing $\theta_{n+1} \sim F(\mu(\theta_n), \Sigma)$ where the $\mu $ is a location vector and $\Sigma$ is a scale matrix. When ...
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Why volume preservation is important for Metropolis update? [duplicate]

I think my question is naive but I would like to ask why why volume preservation is important for MCMC and specifically Metropolis update.I'm reading the following paper https://arxiv.org/pdf/1206....
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How does the celebrated result about the diffusion limit of the Random Walk Metroplis-Hastings algorithm help us to find the optimal scaling

Let $d\in\mathbb N$ with $d>1$ $\ell>0$ $\sigma_d^2:=\frac{\ell^2}{d-1}$ $f\in C^2(\mathbb R)$ be positive with $$\int f(x)\:{\rm d}x=1$$ and $g:=\ln f$ $Q_d$ be a Markov kernel on $(\mathbb R^...
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1answer
68 views

Proposal in MCMC lives in bigger space than parameter space. Which transformations should I choose?

I'm using a MCMC algorithm. The proposal is, due to lack of information on my part, a multivariate T-Student distribution, i.e. $\theta \sim \mathcal{MT}(\mu, \Sigma)$. However, some of the components ...
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63 views

Is the MC produced by HMC reversible?

I know that the deterministic dynamics in Hamiltonian Monte Carlo/Hybrid Monte Carlo are reversible and the numerical integrators one uses to approximate them are reversible too. But HMC consists of 2 ...
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1answer
49 views

2 versions of Metropolis-Hastings : are they equivalent?

I have seen 2 different versions of Metropolis algorithm. First one : Second one : I don't understand the differences between the 2 versions, especially in the second one where I have to use the ...
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1answer
341 views

Metropolis Hastings - Acceptance ratio, proposal and lkelihood

From a previous post : First to explain the MH algorithm, it's used to approximate numerically a target distribution, in this case $p(\theta|D)$. At each stage of the algorithm: A value ...
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1answer
163 views

How worried should I be about low acceptance rate in cold chain (parallel tempering MCMC sampler)

I have a very noisy/multimodal likelihood function for a 6-parameter model. The popular emcee sampler fails miserably (no matter how many chains I use and for how ...