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.

Filter by
Sorted by
Tagged with
1
vote
0answers
36 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 ...
0
votes
0answers
16 views

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 ...
1
vote
0answers
44 views

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....
5
votes
0answers
95 views

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^...
0
votes
1answer
58 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 ...
2
votes
0answers
49 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
votes
1answer
35 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 ...
0
votes
1answer
172 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 ...
2
votes
1answer
112 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 ...