Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

For more information, see https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method

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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 data. The problem I have with the "true" uniform…
Has QUIT--Anony-Mousse
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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 higher primes especially are often highly…
naught101
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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, so we're left with numerical approximation. But…
MathematicalOrchid
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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 densely cover [0,1] in an incremental fashion). For…
Edouard Poor
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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 $[0,1]$. I can, however, choose the locations where I…
robinson
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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 you some sense of which behaviours are clustered…
Tyler Rinker
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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 replications I want to do. Is it viable to do one latin…
naught101
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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 the expectation of a random variable $X$ such…
jcken
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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 sequences). It seems to me low discrepancy…
Tim
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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, originating partly from random runs, latin hypercube…
Sarmes
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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 having trouble converting this big O notation into…
Scott
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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 chaospy.J(chaospy.Normal(0, 1)), I get an array of…
Kevin K.
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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 probable subspaces", which to me sounds like a…
r00kie
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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-random number generator have such thing as a…
user21186
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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: $$\text{Revenue(t)} = \sum_{i = 1}^t \text{Price}(i) \cdot \text{#Cups}(i),$$ where $\text{Price}(i)$ is the…
Peter
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