# 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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### MCMCglmm package [closed]

the summary() for my ordinal model isn't returning all of my cutpoints. There are four levels in my response variable but I'm only getting two cut points. Does anyone know why?
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### Jacobian and proposal ratio of Birth/death step in RJMCMC of Gaussian mixture model

I am asking questions regarding RJMCMC several times in this site. Some of my questions are answered and some are unanswered. It didn't clarify all of my unclear points but I am glad that I have ...
1 vote
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### Is Metropolis-Hastings ever more efficient than rejection sampling in 2 dimensions?

I know that Metropolis-Hastings is an MCMC (Markov Chain Monte Carlo) method that is very useful in higher dimensions. The advantages it has over something like simple rejection sampling are that ...
44 views

### Random scan Gibbs sampling as special case of Metropolis-Hastings

I am reading Blitzstein's Introduction to Probability and come across with the following proof that I don't really understand: Theorem: The random scan Gibbs sampler is a special case of the ...
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### Is it possible to increase the Hastings ratio by combining and mixing elementary kernels?

Let's say I am working with a state $X$ split into three parts $U$, $V$, and $W$. I can efficiently sample from $W|U,V$, $U|V$, and $V|U$. My initial intuition was to do a variable-at-a-time ...
84 views

### Computational aspect of the Metropolis-Hastings algorithm

One of the examples online is about how to write the Metropolis-Hastings algorithm from scratch. This tutorial uses a linear regression model as an example. Estimate three parameters: an intercept, a ...
42 views

### Metropolis Hastings Algorithms: How to measure the performance of algorithms? (Multidimensional)

I am working on a project and I am trying to measure the performance and compare two MCMC algorithms. The one is Random-Walk MH and the second one is PCN. I thought of maybe comparing the mean ...
163 views

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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 ...
278 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 ...
1 vote
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### 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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1 vote
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### 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 ...
180 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 ...
1 vote
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### 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 ... 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 ... 