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Are these the same as quasi-random or sub-random sequences (that terminology is used in Numerical Recipes)? If so it would be good to say so. Josh Cherry 23:10, 15 May 2004 (UTC)
Hi,
This page should have a reference to Jurjen Ferdinand Koksma, after whom some of the items on this page are named. He was a professor at the University of Amsterdam.
Hello, I wonder if we can put in the discrepancy calculated for some examples. E.g. uniform distribution of points, pseudo-random, maybe some other patterns. I think that those examples would shed some light on low-discrepancy sequences in comparison. Have a good day. 64.48.193.123 18:36, 15 January 2006 (UTC)
Is there perhaps an error in the definition given in the first sentence? It says, "for all N, the subsequences x1, ..., xN and x1, ..., xN+1 are almost uniformly distributed." But that x1, ..., xN+1 is almost uniformly distributed follows immediately from the fact thet x1, ..., xN is (for all N), when used for N + 1. -- Meni Rosenfeld ( talk) 13:12, 15 August 2006 (UTC)
I've created discrepancy of a sequence as a redirect "with possibilities". I'm thinking of moving some of the definitions and properties from here and from equidistributed sequence across to make that into a proper article. Richard Pinch ( talk) 06:26, 19 August 2008 (UTC)
What is
(in Definition of discrepancy). Is it an intersection of sets / intervals? Then one should be using . TomyDuby ( talk) 02:38, 26 September 2008 (UTC)
It seems to me that the new article subrandom numbers should be merged here. Is anyone willing and able to do this? Sławomir Biały ( talk) 11:48, 7 April 2011 (UTC)
There seems to reason for that to be a separate article. Deltahedron ( talk) 16:52, 26 August 2012 (UTC)
In the article it is said that since the KH inequality is sharp
"... the quality of a numerical integration rule depends only on the discrepancy D*N(x1,...,xN)."
I think that may lead people to wrong conclusions, as it's is valid only, if all that you know about the function to integrate is, that it has bounded variation. If you know more (e.g. continuity, differentiability, ...) there may indeed be better integration rules. Thus I would like to extend the sentence a little bit in that sense. Would that be ok? Ezander ( talk) 16:58, 28 November 2012 (UTC)
Per the talk page suggestion by Deltahedron, I've boldly merged the prose from Constructions of low-discrepancy sequences into this article and rearranged the sections a bit. With two merges, there is more work to be done to get the article flowing nicely. -- Mark viking ( talk) 00:35, 20 February 2014 (UTC)
Over the past few months, people seem to have removed the most useful information from the "Additive recurrence" section, namely a couple good examples that are valid and easily verifiable. When I happened upon this page before, I checked them, and they were indeed both better than the ones I'd already found; it's information that's hard to find but easy to verify. When I came back to this page today to check what the numbers were, (because I needed a good additive recurrence sequence again), the examples had been removed. Nobody is about to remove the useful examples on the Taylor series page for lack of citations, because they're easily verifiable, correct, and useful examples, so I'm going to add these easily verifiable, correct, and useful examples back. The importance of always using different coefficients for each dimension in multiple dimensions is also critical to note, since you'll effectively lose an entire dimension of coverage if even two of them are the same.
Sure enough, a highly misleading (effectively incorrect) sentence has also been added: "Note, however, that such a generator is known to have severe statistical flaws. The list of pseudorandom number generators provides better alternatives." It appears that someone was under the incorrect impression that the purpose of the additive recurrence is to generate independent random numbers, which is not at all the case. The entire point of low discrepancy sequences is to have better coverage than independent random numbers, so pseudorandom number generators are not "better alternatives" at all, and there is no "statistical flaw", let alone a "severe" one. They produce significantly higher discrepancy sequences. I'll change this sentence to a clarification that this does not generate random numbers, even though it's made fairly clear in the introduction of the article.
If anyone takes issue with these changes, please discuss here. Ndickson ( talk) 03:49, 13 September 2014 (UTC)
A comment related to the topic "Additive recurrence": I am aware that an earlier contributor has done a thorough optimization study, and concluded that c1 = 0.5545497, c2 = 0.308517 are optimal for 2D additive recurrence sequences. However, some of this documentation seems to have been removed by later edits, and only the 2D figure remains, with caption text. I do not know which discrepancy criterion was used by the contributor. It would therefore be greatly appreciated if any contributor can add documentation about the source of these two coefficients (or re-calculate them), together with the discrepancy criterion. — Preceding unsigned comment added by Peter.schild ( talk • contribs) 07:27, 19 July 2022 (UTC)
Hi, should LHS appear there ? 195.83.81.127 ( talk) 13:35, 24 October 2014 (UTC)
The section Low-discrepancy_sequence#Random_numbers has no citations, and I think it's basically totally wrong. Meaning, alternating between r_i and r_i + 1/2 will reduce your discrepancy almost not at all compared to drawing samples from the full uniform distribution. Any objections to me removing the section? Danstronger ( talk) 00:43, 1 February 2020 (UTC)
A discussion is taking place to address the redirect
QRNG. The discussion will occur at
Wikipedia:Redirects for discussion/Log/2021 December 8#QRNG until a consensus is reached, and readers of this page are welcome to contribute to the discussion.
Chumpih. (
talk)
08:02, 8 December 2021 (UTC)
This article is filled with "Examples" of QMC sequences using invalid sample sizes. Using a Sobol sequence with 1,000 points, for example, is incorrect, as Sobol sequences must have exactly 2^n points. Using non-powers of 2 destroys the (t, m, s)-net (equidistribution) property, which is what guarantees faster convergence than you get from pseudo-random numbers. Closed Limelike Curves ( talk) 00:48, 28 September 2022 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Are these the same as quasi-random or sub-random sequences (that terminology is used in Numerical Recipes)? If so it would be good to say so. Josh Cherry 23:10, 15 May 2004 (UTC)
Hi,
This page should have a reference to Jurjen Ferdinand Koksma, after whom some of the items on this page are named. He was a professor at the University of Amsterdam.
Hello, I wonder if we can put in the discrepancy calculated for some examples. E.g. uniform distribution of points, pseudo-random, maybe some other patterns. I think that those examples would shed some light on low-discrepancy sequences in comparison. Have a good day. 64.48.193.123 18:36, 15 January 2006 (UTC)
Is there perhaps an error in the definition given in the first sentence? It says, "for all N, the subsequences x1, ..., xN and x1, ..., xN+1 are almost uniformly distributed." But that x1, ..., xN+1 is almost uniformly distributed follows immediately from the fact thet x1, ..., xN is (for all N), when used for N + 1. -- Meni Rosenfeld ( talk) 13:12, 15 August 2006 (UTC)
I've created discrepancy of a sequence as a redirect "with possibilities". I'm thinking of moving some of the definitions and properties from here and from equidistributed sequence across to make that into a proper article. Richard Pinch ( talk) 06:26, 19 August 2008 (UTC)
What is
(in Definition of discrepancy). Is it an intersection of sets / intervals? Then one should be using . TomyDuby ( talk) 02:38, 26 September 2008 (UTC)
It seems to me that the new article subrandom numbers should be merged here. Is anyone willing and able to do this? Sławomir Biały ( talk) 11:48, 7 April 2011 (UTC)
There seems to reason for that to be a separate article. Deltahedron ( talk) 16:52, 26 August 2012 (UTC)
In the article it is said that since the KH inequality is sharp
"... the quality of a numerical integration rule depends only on the discrepancy D*N(x1,...,xN)."
I think that may lead people to wrong conclusions, as it's is valid only, if all that you know about the function to integrate is, that it has bounded variation. If you know more (e.g. continuity, differentiability, ...) there may indeed be better integration rules. Thus I would like to extend the sentence a little bit in that sense. Would that be ok? Ezander ( talk) 16:58, 28 November 2012 (UTC)
Per the talk page suggestion by Deltahedron, I've boldly merged the prose from Constructions of low-discrepancy sequences into this article and rearranged the sections a bit. With two merges, there is more work to be done to get the article flowing nicely. -- Mark viking ( talk) 00:35, 20 February 2014 (UTC)
Over the past few months, people seem to have removed the most useful information from the "Additive recurrence" section, namely a couple good examples that are valid and easily verifiable. When I happened upon this page before, I checked them, and they were indeed both better than the ones I'd already found; it's information that's hard to find but easy to verify. When I came back to this page today to check what the numbers were, (because I needed a good additive recurrence sequence again), the examples had been removed. Nobody is about to remove the useful examples on the Taylor series page for lack of citations, because they're easily verifiable, correct, and useful examples, so I'm going to add these easily verifiable, correct, and useful examples back. The importance of always using different coefficients for each dimension in multiple dimensions is also critical to note, since you'll effectively lose an entire dimension of coverage if even two of them are the same.
Sure enough, a highly misleading (effectively incorrect) sentence has also been added: "Note, however, that such a generator is known to have severe statistical flaws. The list of pseudorandom number generators provides better alternatives." It appears that someone was under the incorrect impression that the purpose of the additive recurrence is to generate independent random numbers, which is not at all the case. The entire point of low discrepancy sequences is to have better coverage than independent random numbers, so pseudorandom number generators are not "better alternatives" at all, and there is no "statistical flaw", let alone a "severe" one. They produce significantly higher discrepancy sequences. I'll change this sentence to a clarification that this does not generate random numbers, even though it's made fairly clear in the introduction of the article.
If anyone takes issue with these changes, please discuss here. Ndickson ( talk) 03:49, 13 September 2014 (UTC)
A comment related to the topic "Additive recurrence": I am aware that an earlier contributor has done a thorough optimization study, and concluded that c1 = 0.5545497, c2 = 0.308517 are optimal for 2D additive recurrence sequences. However, some of this documentation seems to have been removed by later edits, and only the 2D figure remains, with caption text. I do not know which discrepancy criterion was used by the contributor. It would therefore be greatly appreciated if any contributor can add documentation about the source of these two coefficients (or re-calculate them), together with the discrepancy criterion. — Preceding unsigned comment added by Peter.schild ( talk • contribs) 07:27, 19 July 2022 (UTC)
Hi, should LHS appear there ? 195.83.81.127 ( talk) 13:35, 24 October 2014 (UTC)
The section Low-discrepancy_sequence#Random_numbers has no citations, and I think it's basically totally wrong. Meaning, alternating between r_i and r_i + 1/2 will reduce your discrepancy almost not at all compared to drawing samples from the full uniform distribution. Any objections to me removing the section? Danstronger ( talk) 00:43, 1 February 2020 (UTC)
A discussion is taking place to address the redirect
QRNG. The discussion will occur at
Wikipedia:Redirects for discussion/Log/2021 December 8#QRNG until a consensus is reached, and readers of this page are welcome to contribute to the discussion.
Chumpih. (
talk)
08:02, 8 December 2021 (UTC)
This article is filled with "Examples" of QMC sequences using invalid sample sizes. Using a Sobol sequence with 1,000 points, for example, is incorrect, as Sobol sequences must have exactly 2^n points. Using non-powers of 2 destroys the (t, m, s)-net (equidistribution) property, which is what guarantees faster convergence than you get from pseudo-random numbers. Closed Limelike Curves ( talk) 00:48, 28 September 2022 (UTC)