Talk:Low-discrepancy sequence

message: 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)
replies: text: Hi Josh. Yes, they are the same. I have added quasi-random and sub-random as synomyms, and put NR on the list of references. The NR discussion will probably be more comprehensible to many readers. I've also made quasi-random, sub-random, quasirandom, and subrandom redirect to low-discrepancy sequence in an effort to head of duplication of the topic. Hope this helps, Wile E. Heresiarch 16:17, 16 May 2004 (UTC)

message: 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)
thread_title:  Explicit discrepancy calculations 

message: 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)
replies: text: I noticed the same. Further, the intro promises that the notion "almost uniformly distributed" will be made precise, but it is never defined. Presumably the definition is something like "having a low discrepancy", but, although "discrepancy" ("Star-Discrepancy"?) is defined (in an unnecessarily hard-to-understand way; what the h*** is "Niederreiter's notation"?), it is never defined what counts as "low" here. Also, presumably, it is a stronger notion than equidistributed, but no relation is made. --LambiamTalk 21:50, 16 August 2006 (UTC)
thread_title:  Error in definition? 

message: 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)
thread_title:  Rearrangement 

message: What is
: \prod_{i=1}^s [a_i, b_i) 
(in Definition of discrepancy). Is it an intersection of sets / intervals? Then one should be using \cap .
TomyDuby (talk) 02:38, 26 September 2008 (UTC)
replies: text: It's an s-dimensional interval or box which is the Cartesian product of s one-dimensional half-open half-closed intervals.  I've expanded the definition in the article.  Richard Pinch (talk) 05:51, 26 September 2008 (UTC)
thread_title:  Clarification needed 

message: There seems to reason for that to be a separate article.  Deltahedron (talk) 16:52, 26 August 2012 (UTC)
thread_title:  [[Constructions of low-discrepancy sequences]] 

message: 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)
thread_title:  Conclusion from Koksma-Hlawka 

message: 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)
replies: text: Per WP:MTAA it might be an idea to put the concrete examples first, to motivate the subject in a qualitative way, before the presentation of the more general theoretical results. Jheald (talk) 07:54, 20 February 2014 (UTC)
thread_title:  Merge from [[Constructions of low-discrepancy sequences]] 

message: 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)
thread_title:  Missing documentation of the 2D sequence in the figure (c<sub>1</sub> = 0.5545497, c<sub>2</sub> = 0.308517) 

message: Hi, should LHS appear there ?195.83.81.127 (talk) 13:35, 24 October 2014 (UTC)
replies: text: Latin hypercube sequences? If so, there are sources out there comparing the utility of LHS and LDS in Monte Carlo simulations, so I think it would be appropriate to include a summary of those comparisons. Latin squares are already mentioned in the article. --Mark viking (talk) 16:04, 24 October 2014 (UTC)
thread_title:  LHS 

message: 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)
thread_title:  "Random numbers" section 

message: 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)
thread_title:  "QRNG" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: 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)
replies: text: +1 here. Art Owen wrote a paper about it, see Owen2020 for extended discussions. Tupui (talk) 09:17, 24 February 2023 (UTC)
thread_title:  Using Incorrect Sample Sizes