Comments - Introduction to Monte Carlo Methods - AnalyticBridge2021-06-25T09:29:10Zhttps://www.analyticbridge.datasciencecentral.com/profiles/comment/feed?attachedTo=2004291%3ABlogPost%3A330772&xn_auth=noAlex, what I have in mind is…tag:www.analyticbridge.datasciencecentral.com,2015-08-04:2004291:Comment:3310142015-08-04T23:09:25.240ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Alex, what I have in mind is to create synthetic numbers that have fast/efficient series expansions (like Pi) or basic recurrence formulas to generate the digits (like SQRT{n} for small n), to generate/reproduce the randomness that these famous numbers exhibit. My hope is to come up with trillions of trillions of trillions of synthetic numbers by modifying parameters associated with the nice or exploitable mathematical formulas available for famous numbers, hoping that my synthetic numbers…</p>
<p>Alex, what I have in mind is to create synthetic numbers that have fast/efficient series expansions (like Pi) or basic recurrence formulas to generate the digits (like SQRT{n} for small n), to generate/reproduce the randomness that these famous numbers exhibit. My hope is to come up with trillions of trillions of trillions of synthetic numbers by modifying parameters associated with the nice or exploitable mathematical formulas available for famous numbers, hoping that my synthetic numbers will be as random as the famous numbers, when it comes to the distribution of digits or decimals. </p> Alex, It has to do with low d…tag:www.analyticbridge.datasciencecentral.com,2015-08-04:2004291:Comment:3309102015-08-04T16:38:01.969ZJohn MacCuishhttps://www.analyticbridge.datasciencecentral.com/profile/JohnMacCuish
<p>Alex, It has to do with low discrepancy sets in small dimensions. See <a href="https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method" target="_blank">https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method</a></p>
<p>They show how to mix pseudo and quasi to generate sets that perform well in higher dimensions.</p>
<p>A great book on monte carlo methods and random number generation in general is </p>
<p>Random Number Generation and Monte Carlo Methods, by Gentle…</p>
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<p>Alex, It has to do with low discrepancy sets in small dimensions. See <a href="https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method" target="_blank">https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method</a></p>
<p>They show how to mix pseudo and quasi to generate sets that perform well in higher dimensions.</p>
<p>A great book on monte carlo methods and random number generation in general is </p>
<p>Random Number Generation and Monte Carlo Methods, by Gentle</p>
<p><a href="http://www.amazon.com/Random-Generation-Methods-Statistics-Computing/dp/0387001786" target="_blank">http://www.amazon.com/Random-Generation-Methods-Statistics-Computing/dp/0387001786</a></p>
<p>Enjoy! :*)</p> Vincent - Very cool. It seems…tag:www.analyticbridge.datasciencecentral.com,2015-08-04:2004291:Comment:3308142015-08-04T16:14:06.709ZAlex Woodshttps://www.analyticbridge.datasciencecentral.com/profile/AlexWoods
<p>Vincent - Very cool. It seems like any of the doubts I had about it you addressed with the tests (in your article). Definitely enjoyed that article.</p>
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<p>John - Great suggestion! I tried it; it worked. Why?</p>
<p>Vincent - Very cool. It seems like any of the doubts I had about it you addressed with the tests (in your article). Definitely enjoyed that article.</p>
<p></p>
<p>John - Great suggestion! I tried it; it worked. Why?</p> I also wrote a bit about rand…tag:www.analyticbridge.datasciencecentral.com,2015-08-01:2004291:Comment:3308982015-08-01T18:26:54.072ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>I also wrote a bit about random generators, <a href="http://www.datasciencecentral.com/page/search?q=random+numbers" target="_blank">see here</a>. My interest is in using decimals of some irrational numbers (Pi has an easy, fast formula to generate decimals, I'm working on a formula for SQRT{2}), as well as synthetic numbers designed to simulate randomness, and period-free.</p>
<p>I also wrote a bit about random generators, <a href="http://www.datasciencecentral.com/page/search?q=random+numbers" target="_blank">see here</a>. My interest is in using decimals of some irrational numbers (Pi has an easy, fast formula to generate decimals, I'm working on a formula for SQRT{2}), as well as synthetic numbers designed to simulate randomness, and period-free.</p> The R randtoolbox package has…tag:www.analyticbridge.datasciencecentral.com,2015-07-31:2004291:Comment:3308872015-07-31T22:02:43.141ZJohn MacCuishhttps://www.analyticbridge.datasciencecentral.com/profile/JohnMacCuish
<p>The R randtoolbox package has a nice set of quasi-random sequence generators, such that if you substitute, say, the "halton" function for "runif" in your code, you will see that the error converges far more quickly. For small dimensions (say, up to 5 dimension), in practice the quasi-random sequences as point generators have much better convergence.</p>
<p>The R randtoolbox package has a nice set of quasi-random sequence generators, such that if you substitute, say, the "halton" function for "runif" in your code, you will see that the error converges far more quickly. For small dimensions (say, up to 5 dimension), in practice the quasi-random sequences as point generators have much better convergence.</p>