# Questions tagged [quasi-monte-carlo]

quasi monte carlo is a technique for doing monte carlo integration and other monte carlo simulations, replacing the usual pseudo random sequence with a low-discrepancy sequence. This can be seen as a general trick to lower the variance introducing dependency into the random number sequence.

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### How to calculate Quasi-Monte Carlo integration error when sampling with Sobol's sequence?

My understanding is that QMC integration using random sampling will converge with $O(\frac{1}{\sqrt{n}})$, while using Sobol's sampling will converge with $O(\frac{(\log{n})^d}{n})$. However I'm ...
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### What are some methods to choose a $n$ for Quasi Monte Carlo Integrations?

When studying "simple" Monte Carlo integration methods, such as Hit or Miss, Crude , Importance Sampling, etc. A common problem for first time learners is to choose a number $n$ of points ...
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### Quasi Monte Carlo estimation of logit-normal density integrals

I am considering the integral $$I(y \mid \mu, \sigma) = \int_y^1 \frac{\exp \left\{ \frac{-1}{2\sigma^2}[\textrm{logit}(x)-\mu)]^2 \right\}}{\sigma \sqrt{2\pi} (1-x)}\textrm{d}x$$ which for $y=0$ is ...
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### Quasi-random sequence with discrete variables with differing number of levels

My question is probably worded incorrectly but here it is: I have (say) 3 discrete random variables: x1: has 15 levels (uniform pdf for simplicity) x2: has 3 levels (uniforms) x3: has 4 levels (...
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### How to get normally distributed Quasi-random numbers

I've been trying to use the chaospy package to get quasi-random numbers for a Monte Carlo simulation. The dimensions need to be 365×5000 (but can be up to 2190×5000). When I pull a sample using ...
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### Stratified sampling / QMC simulation for compound Poisson rv

I have a rv $X$ of the form $$X=\sum_{i=1}^N Y_i,$$ where $N$ is a discrete rv (often, but not always, Poisson) and $Y_1,\ldots,Y_N$ are continuous random variables, iid and independent from $N$. I ...
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1 vote
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### Inverse transform method on MCMC generated uniform draws

I understand that it sounds like why would anyone do this, but are there any references that use the inverse transform method to draw correlated samples from a distribution $F$ using MCMC samples from ...
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1 vote
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### Are subsequences of low discrepancy sequence also low discrepancy? [closed]

Given a low discrepancy sequence x1 ... xN, lets say I randomly select a subsequence x100 ... x200, will this subsequence have low discrepancy? Will those points "fill" up the space uniformly? If not ...
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### How to apply linear transformation? [closed]

In this post, Martin Roberts mentioned that: ... to convert to a range of [-1,1], simply apply the linear transformation x:=2x+1. The result is (-0.361655, -0.657913, -0.900599) (-0.72331, 0.684174, ...
1 vote
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### Can/should one generate Ginibre ensembles of random matrices using low-discrepancy normal variates--and if so. how?

I've been generating (via Mathematica) series of $4 \times 4$ "random density matrices with respect to Bures (minimal monotone) measure" https://arxiv.org/abs/0909.5094 [eq. (24)] and testing certain ...
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### Sobol Sensitivity Analysis

I want to use Sobol SA with Sobol sampling to find the most influential parameters on the energy consumption of a pilot building. I have 40 input variables (building characteristics) that some have ...
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### How to estimate the accuracy of an integral?

An extremely common situation in computer graphics is that the colour of some pixel is equal to the integral of some real-valued function. Often the function is too complicated to solve analytically, ...
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### Best method for transforming low discrepancy sequence into normal distribution?

I've been using low discrepancy sequences for a while for Uniform Distributions, as I've found their properties useful (mainly in computer graphics for their random appearance and their ability to ...
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### Halton sequence vs Sobol' sequence?

From an answer in a previous question, I was directed toward the Halton sequence, for creating a set of vectors that covered a uniform sample space fairly evenly. But the wikipedia page mentions that ...
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### Increase the sample size of a Latin Hypercube study?

I want to create a climate model ensemble, testing 5 parameters (real, uniformly distributed between two values), using a latin hypercube approach. The problem is that I'm not sure how many ...
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