Skip to main content

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.

Filter by
Sorted by
Tagged with
1 vote
0 answers
19 views

Does it make sense to compare $KL(q_1|p)$ vs $KL(q_2|p)$ where $q_1$ and $q_2$ are empirical distributions?

I simulated x samples of N(0,1) using Sobol sequence vs 100x samples of N(0,1) peuso-random number. I chopped up simulations to 100 samples for peudo-random number. I found about 50 times the KL ...
Lost1's user avatar
  • 656
0 votes
0 answers
10 views

Quasi Monte Carlo: Is not grid search the ultimate low discrepancy sequence?

I realize that subsequences won't be low discrepancy, but if I know how many samples I want and that I am operating on the unit hypercube, why not just grid search as the low discrepancy sequence in ...
lware's user avatar
  • 21
1 vote
0 answers
25 views

Generation of completely uniformly distributed sequences

In quasi-Monte Carlo, there is a rather strong notion "completely uniformly distributed" sequences, which somehow mimics independence and is described, for example, at the end of this post. ...
0xbadf00d's user avatar
  • 293
2 votes
1 answer
118 views

Is there a Quasi-Monte Carlo variant of the Metropolis-Hastings algorithm?

If we run the Metropolis-Hastings algorithm for a target distribution $\mu$ with proposals from a quasi-Monte Carlo sequence $(y_n)_{n\in\mathbb N}$ (such as a Sobol sequence) and the generated chain ...
0xbadf00d's user avatar
  • 293
1 vote
0 answers
47 views

"Variance" estimate for quasi-Monte Carlo

Problem Setting I am playing with a toy example and I would like to better understand the variance results that I get when using low-discrepancy sequences versus random values. I have independent and ...
lightxbulb's user avatar
4 votes
2 answers
616 views

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 ...
Scott's user avatar
  • 173
1 vote
0 answers
104 views

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 ...
Telihcirid's user avatar
4 votes
1 answer
146 views

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 ...
jcken's user avatar
  • 2,907
2 votes
1 answer
146 views

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 (...
Sri's user avatar
  • 21
3 votes
1 answer
704 views

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 ...
Kevin K.'s user avatar
  • 131
1 vote
1 answer
183 views

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 ...
AndreA's user avatar
  • 237
2 votes
1 answer
85 views

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 ...
Greenparker's user avatar
  • 15.6k
1 vote
0 answers
24 views

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 ...
Jason's user avatar
  • 11
0 votes
1 answer
73 views

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, ...
user10608907's user avatar
1 vote
1 answer
190 views

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 ...
Paul B. Slater's user avatar
1 vote
1 answer
1k views

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 ...
Maryam Nahid's user avatar
2 votes
1 answer
53 views

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 ...
Peter's user avatar
  • 21
0 votes
1 answer
38 views

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 ...
GeoH2O's user avatar
  • 111
1 vote
0 answers
137 views

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 ...
Bart Plovie's user avatar
1 vote
0 answers
105 views

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 ...
user315648's user avatar
2 votes
0 answers
92 views

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-...
user avatar
3 votes
1 answer
299 views

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, ...
Sarmes's user avatar
  • 151
8 votes
1 answer
224 views

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 ...
Tyler Rinker's user avatar
48 votes
5 answers
6k 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 ...
Has QUIT--Anony-Mousse's user avatar
4 votes
2 answers
768 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 ...
Tim's user avatar
  • 19.5k
9 votes
2 answers
2k views

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 $[0,1]$...
robinson's user avatar
  • 423
11 votes
2 answers
2k views

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, ...
MathematicalOrchid's user avatar
15 votes
4 answers
7k views

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 ...
Edouard Poor's user avatar
15 votes
1 answer
5k views

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 ...
naught101's user avatar
  • 5,453
7 votes
1 answer
2k views

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 ...
naught101's user avatar
  • 5,453
4 votes
1 answer
1k views

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 ...
r00kie's user avatar
  • 91