Tagged Questions

Importance sampling is a variance reduction technique to approximate integrals/expectations which are not directly computable.

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In importance sampling, why should the importance density have heavier tails?

Why should the importance density (or biasing density) $g$ have heavier tails than the original distribution $f$? Equivalently, why should $$\frac{f(x)}{g(x)}<M , \forall x$$ for some $M>0$?
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Estimating Bayes factor in moderately high dimension (about 100)

There is a large literature about the estimation of bayes factor using e.g. importance sampling (e.g. https://www.rocq.inria.fr/axis/COMPSTAT2010/TU-marin_paper.pdf). Most (all?) of them investigate ...
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Outliers in importance sampling

I'm working on a HW question in which I'm using importance sampling method to estimate E(X) where X is distributed as standard Laplace. To do so, I choose my proposal density to be standard normal. I ...
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Importance sampling of finite path of stochastic difference equation

Before passing to question, let me briefly recap what's importance sampling of random variables is about. Suppose $\xi$ is a real-valued random variable with density $f$, and let $g:\Bbb R\to \Bbb R$ ...
I've got two algorithms, $A$ and $B$, I want to evaluate. Both algorithms differ by the distribution of points they produce. Let us suppose that $A$ generates points from $P_S$ distribution while B ...