# Questions tagged [importance-sampling]

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

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### Effective samples size for quantile estimates with weighted samples

I've been reading the paper Rethinking the Effective Sample Size. In it, the authors provide an estimator for effective sample size given weighted samples (eq. 5.1 in the paper) which specifically ...
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### Simplying Bayes Theorem expression: SIS particle filter posteriori

In the book Beyond the Kalman Filter: Particle Filters for Tracking Applications on page 39 the weight update equation for the particle filter is derived. The derivations begins by introducing the ...
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### Is there any proof of global convergence for 1D convex numeric optimization using cross entropy method?

Suppose we have the following 1D numeric optimization problem: $min_{x} f(x)$ given $0< x \le x_{MAX}$ where $f(x)$ is a convex function. And I want to apply the cross-entropy method to optimize ...
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### Particle filter: Evaluating Optimal importance density

NOTE I posted this in the math stack exchange but I realized this may be the more appropriate place, old post here. I'm not sure if I should delete one of them so I just linked them in both? I am ...
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### Estimate default by importance sampling (using R)

I want to use Importance sampling to estimate probability of default of an insurance company within the next $t$ years. The company starts with capital $C$ at $t=0$. Each year it gains $p > 0$ ...
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### Stratified sampling to generate random numbers (eg. for Monte-Carlo applications)

I am using a Monte-Carlo method to compute a value of interest $y$ from some input parameters $x_{i}$, that I use to draw statistical sets from simple distribution laws. In my case, for a single Monte-...
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### assessing the stability of importance (sampling) weights

I have read that when importance weights are used, the stability (variability) of the weights should be assessed (Levine and Casella, 2001) -- however, I wonder how this might be accomplished. For ...
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### Can importance sampling be used as an actual sampling mechanism?

This question is a duplicate of How can we use importance sampling for drawing posterior distribution samples? , but that question seems to lack additional detail and goes unanswered (for more than 2 ...
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### Evaluate an integral using importance sampling

Estimate $\int^{1}_{0}e^{x} dx$ using importance sampling. Should I use beta distribution as proposal distribution and uniform distribution as target ?
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### Any papers or unpublished work on relationship of downsample/upweighting and importance sampling in the context of training imbalanced classes

I understood that the general Q of training highly imbalanced data has been asked and answered many times. I have skimmed through the other threads and felt fairly confident my specific question/point ...
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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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### Generating samples from target distribution after importance sampling

So I'm trying to understand importance sampling. So far I have the algorithm implemented like this: ...
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### Literature on design of importance sampling distribution using MLE or point-estimates of highest modes

Suppose I have many distributions $p_i(\theta)$ I wish to take expectations over $$\mathbb{E}_{p_i}[\mathbf{f}_i(\theta)]$$ where the $\mathbf{f}_i$ are vector-valued. In my problem the $p_i$ share ...
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### How to evaluate double Integral with importance sampling

I am trying to recreate the Bayesian Hierarchical Clustering algorithm using Python. The example in section two requires evaluating the following double integral (univariate case): \begin{align} p(...
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### Variance of Monte Carlo integration with importance sampling

I am following these lecture slides on Monte Carlo integration with importance sampling. I am just implementing a very simple example: $\int_{0}^{1} e^{x}dx$. For the importance sampling version, I ...
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### Importance sampling with partly deterministic samples

I am trying to estimate an expectation with a certain set of unlikely, but important (for the value of the expectation) events. In particular, let’s say I have a (normal) distribution p(x). Now, I ...
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### importance sampling from posterior distribution in R

Today I read that Importance Sampling can be used to draw posterior distribution samples just like Rejection Sampling. However, my understanding of Importance Sampling is that its main purpose is to ...
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### importance sampling for conditional probability

Stats experts, I am trying to estimate $G(x)$ for $x$ in a very small subset $A$ of a finite space $U$, i.e $E(G(x | x \in A))$. Determining if $x$ in $A$ has a cost. So it is expensive to uniformly ...
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### in reinforcement learning off policy mc may not work

I noticed off-policy mc prediction(or control) will not work, as being descripted by boxed algorithm in page 110 of the book "reinforcement learning an introduction". The weight W should before C's(...
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### Generalization performance in Bayesian errors-in-covariates model

I'm working on a model with this basic structure: The square nodes are data, and the round nodes are parameters and/or latent variables. The left plate represents the "training observations" we ...
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### Would an “importance Gibbs” sampling method work?

I suspect this is a fairly unusual and exploratory question, so please bear with me. I am wondering if one could apply the idea of importance sampling to Gibbs sampling. Here's what I mean: in Gibbs ...
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### importance sampling and exponential moving average

Lets say i have got a random variable $X$ with samples $x_t\sim X$ and density $p_X(x)$ and want to compute its mean via a moving average $\mu_{t+1}=(1-c)\mu_t + c x_t$ Assume, I can not observe $X$...
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### What's done with the expectations in this proof?

This is a proof of the per-decision importance sampling (theorem 1) from the appendix of: https://www.google.co.uk/url?sa=t&source=web&rct=j&url=http://scholarworks.umass.edu/cgi/...