# 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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### Jacobian term for Metropolis Hastings algorithm?

Suppose an acceptance ratio of the MH sampler without parameter transformation is like this: \begin{gather} r=\frac{f( \theta ',\gamma '|y,m) q( \theta ',\gamma '|\theta ,\gamma )}{f( \theta ,\gamma |...
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### Adaptive MCMC with low acceptance rate

I'm running an MCMC scheme defined in A tutorial on adaptive MCMC. Christophe Andrieu·Johannes Thoms. Stat Comput (2008) 18: 343–373DOI 10.1007/s11222-008-9110-y. They say the optimal scaling factor ...
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### Simulated annealing acceptance probability puzzle

My understanding of simulated annealing (SA) is that at any iteration $t$, a new sample $Y_t$ is generated, which, if the objective function $E$ is improved, i.e., $E(Y_t)<E(X_{t-1})$, then $Y_t$ ...
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### How do we need to define the acceptance ratio of the Metropolis-Hastings algorithm for a vanishing proposal density?

I've seen that different authors define the acceptance probability $\alpha$ of the Metropolis-Hastings algorithm with target distribution density $p$ and proposal kernel density $q$ differently; some ...
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### Can a Metropolis-Hastings estimator converge if the proposal density vanishes whenver the target density vanishes?

I'm running the Metropolis-Hastings algorithm for a target and proposal density $p$ and $q$, respectively, for which it holds $$p(y)=0\Rightarrow q(x,y)=0\;\;\;\text{for all }y.\tag1$$ By definition ...