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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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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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, ...
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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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2 votes
1 answer
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Monte Carlo for revenue model plotted over time

I have a revenue formula for a business. Let’s assume it’s for a lemonade stand. To simplify, assume the revenue formula at any time $t$ is: $$\text{Revenue(t)} = \sum_{i = 1}^t \text{Price}(i) \cdot ...
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How to model variation in different parts of a distribution and understand impact of change of one or more on overall?

I have a very large distribution of real world process values with about 200 odd attributes that can be used to divide it within different parts. This distribution is essentially a time delta ...
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Constrained Quasi-Random Design Methodology

I have a question about a practical design of experiment challenge I'm currently facing for my Ph.D., specifically about the selection of design points to investigate. The severely restricted case I'm ...
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Using low-discrepancy sequence for bernoulli trials in MC sim

I need to generate binomial distribution random numbers for my Carlo simulation (I need Bernoulli trials for a parameter). Thus far, I've used R "rbinom" function for that. However, as I understand, I ...
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2 votes
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Does quasi-random number generator have a period?

I read somewhere, maybe incorrectly, that the Niederreiter quasi-random generator in MKL is 32 bit, and hence as a period of 2^32. This is pretty low, is this correct? This made me wonder if quasi-...
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3 votes
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Selecting uncorrelated samples from a set of bulk data that contains correlated and dependent samples

i have a set of data that is generated by expensive computational model evaluations, on a total data set of 10000 samples in 40 dimensions. This sample data set is composed of different data sets, ...
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8 votes
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What method is simulating pvalues from re sampling from the data

A while back I asked a question about correlating times between time stamps and received a response from Peter Ellis that said I could calculate mean distances between codes... This already will give ...
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43 votes
5 answers
5k views

Fake uniform random numbers: More evenly distributed than true uniform data

I'm looking for a way to generate random numbers that appear to be uniform distributed -- and every test will show them to be uniform -- except that they are more evenly distributed than true uniform ...
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4 votes
2 answers
545 views

Do quasi random number generators sample only uniform distribution?

From Wikipedia quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random ...
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9 votes
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Solving a simple integral equation by random sampling

Let $f$ be a nonnegative function. I am interested in finding $z \in [0,1]$ such that $$ \int_0^{z} f(x)\,dx = \frac{1}{2}\int_0^1 f(x)\,dx$$ The caveat: all I can do is sample $f$ at points in $[0,1]$...
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11 votes
2 answers
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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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10 votes
4 answers
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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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13 votes
1 answer
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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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7 votes
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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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3 votes
1 answer
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Orthogonal sampling, latin hypercubes and low discrepancy sequences

What is the difference between each of them? this wiki page - http://en.wikipedia.org/wiki/Latin_hypercube_sampling says that: "In Orthogonal Sampling, the sample space is divided into equally ...
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