Timeline for Discrepancy of the Halton set
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2022 at 6:10 | history | edited | YCor |
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| Dec 1, 2022 at 1:45 | answer | added | Arturo Ortiz Tapia | timeline score: 1 | |
| Apr 24, 2019 at 21:46 | comment | added | Divakaran Divakaran | ah ok. I see the difference | |
| Apr 24, 2019 at 15:11 | comment | added | Liviu Nicolaescu | How about we split the difference: discrepancy is well defined for finite sets, but it is relevant to Monte Carlo method that deals with sequences. In that case only certain sets are interesting, namely initial segments, i.e., the sets formed by consecutive terms of the sequence. | |
| Apr 24, 2019 at 14:08 | comment | added | Divakaran Divakaran | Moreover, once we have confirmed that the sequence is equidistributed, should we not look at the discrepancy of the set? | |
| Apr 24, 2019 at 14:06 | comment | added | Divakaran Divakaran | @LiviuNicolaescu I guess I understand a bit better. But, I still share GerryMyerson‘s doubt | |
| Apr 24, 2019 at 0:02 | comment | added | Liviu Nicolaescu | The moment you wrote initial segments you assume that the elements of the set are indexed $x_1,\dotsc, x_n,...$. "A rose by any other name would smell as sweet" | |
| Apr 23, 2019 at 22:55 | comment | added | Gerry Myerson | The m.se post can be found at math.stackexchange.com/questions/3186682/… | |
| Apr 23, 2019 at 22:53 | comment | added | Gerry Myerson | @Liviu, I reckon Monte-Carlo implementations use initial segments of sequences, which amounts to using finite sets, and the discrepancy of these finite sets is an important consideration in these implementations. | |
| Apr 23, 2019 at 19:22 | comment | added | Liviu Nicolaescu | Equidistribution is a property of sequences since its formulation involves limits. | |
| Apr 23, 2019 at 19:13 | comment | added | Liviu Nicolaescu | The basis of the Monte-Carlo method is the theorem $$\lim_{n\to\infty}\frac{1}{n}(f(X_1)+\cdots +X_n)=\int_0^1 f(x) dx, $$ almost surely, where $(X_n)$ is a sequence of independent random variables, uniformly distributed over $[0,1]$. | |
| Apr 23, 2019 at 14:38 | comment | added | Divakaran Divakaran | @LiviuNicolaescu can you explain? It seems to me that Monte Carlo integration uses sets. | |
| Apr 23, 2019 at 13:59 | history | edited | Divakaran Divakaran | CC BY-SA 4.0 |
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| Apr 23, 2019 at 13:56 | comment | added | Liviu Nicolaescu | Monte-Carlo implementations use sequences rather than sets. then what you are generating is a | |
| Apr 23, 2019 at 13:19 | history | asked | Divakaran Divakaran | CC BY-SA 4.0 |