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Tagged with importance-sampling metropolis-hastings
5 questions
0
votes
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Metropolis sampling with stochastic estimation of component of probability density
Consider the probability distribution
\begin{align}
p(x) = \frac{1}{Z} x^2 e^{-x^2 / 2}
\end{align}
where $x \in \mathbb{R}$ and $Z$ is a normalization factor so that $\int_{-\infty}^{\infty} dx \, p(...
- 133
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Multiple Importance Sampling and Metropolis-Hastings on extended state space
Let
$(E,\mathcal E,\lambda),(E',\mathcal E',\lambda')$ be measure spaces
$k\in\mathbb N$
$p,q_1,\ldots,q_k:E\to(0,\infty)$ be probability densities on $(E,\mathcal E,\lambda)$
$w_1,\ldots,w_k:E\to[0,...
- 213
3
votes
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45
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Is there a reason why we should run the Metorpolis-Hastings algorithm with a target density approximating the density we're actually after?
Let $(E,\mathcal E,\lambda)$ be a measure space, $p:E\to[0,\infty)$ be $\mathcal E$-measurable with $$c:=\int p\:{\rm d}\lambda$$ and $$\mu:=\underbrace{\frac1cp}_{=:\:\tilde p}\lambda$$ denote the ...
- 213
51
votes
1
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What is the difference between Metropolis-Hastings, Gibbs, Importance, and Rejection sampling?
I have been trying to learn MCMC methods and have come across Metropolis-Hastings, Gibbs, Importance, and Rejection sampling. While some of these differences are obvious, i.e., how Gibbs is a special ...
- 2,425
4
votes
1
answer
2k
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Independence-Metropolis-Hastings Algorithm
IMHA is an importance-sampling version of MCMC, where the proposal is drawn from a fixed distribution g. Usually, g is chosen to be an approximation to f. The acceptance probability becomes
$r(x,y)=\...
- 537