# Questions tagged [importance-sampling]

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

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### Single-sample self-normalized importance weighting

Self-normalizing sampling schemes (https://artowen.su.domains/mc/Ch-var-is.pdf) seem to require at least two samples to give non-trivial weightings under an importance sampling distribution. Is there ...
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### On the optimal distribution for importance sampling

Let's say $X$ is a rv, $p(x)$ is its pmf. I want to importance-sample $\mu := \mathbb E[f(X)]$, for some bounded function $0<f<1$, using another distribution $q(x)$. Then what I should do is ...
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### Calculating the weights in ABC SMC (2 parameters and more)

Im trying to implement ABC SMC for ODE model which has 2 parameters to estimate. I stopped in the step when calculating the weights as it appear in this answer. My question is should I calculate the ...
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### Bootstrap Particle Filter (Gordon, Salmond, Smith, 2003) - Importance Weights

So, my endeavor to apply the is just for my own edificationI am currently struggling with an attempt to apply a bootstrap particle filter (Gordon, Salmond, Smith, 2003) to a linear, Gaussian state-...
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### Why does weighted importance sampling work?

I am reading Sutton & Barto. I am trying to understand this passage from chapter 5: An important alternative is weighted importance sampling, which uses a weighted average, defined as  V (...
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### Importance Sampling derivation

I'm learning about importance sampling from p139 of this book which has the following derviation: What I am confused about is the second step in the derivation, though the rest makes sense to me. I ...
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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,...