Re: Sobol's Low discrepency sequence

Posted by Mark joshi-2 on
URL: http://quantlib.414.s1.nabble.com/Sobol-s-Low-discrepency-sequence-tp5905p5908.html

I don't think anyone really discusses the reasoning behind their
orderings. One of the original papers (Bratley Fox) used a non-obvious
ordering which was followed for a while.
Later on, people, including Peter Jaeckel, switched to using ascending order.

The reference list in the sobolrsg.hpp is pretty comprehensive.

regards

Mark

On 25/03/2008, Lecuyer, Fabrice <[hidden email]> wrote:

> Thanks Mark.
>
>  Could you please point me to a paper/book that explains the ordering for the polynomials used in QuantLib?
>
>  Regards,
>  Fabrice
>
>  -----Original Message-----
>  From: Luigi Ballabio [mailto:[hidden email]]
>  Sent: Monday, 24 March 2008 11:51 PM
>  To: Lecuyer, Fabrice; Mark joshi
>  Cc: [hidden email]
>  Subject: Re: [Quantlib-users] Sobol's Low discrepency sequence
>
>
>  On Mar 20, 2008, at 3:06 AM, Lecuyer, Fabrice wrote:
>  > I'm working through the implementation of the Sobol number generator
>  > in QuantLib and I've got two questions on which I would appreciate any
>  > insight you can give me:
>  >
>  > 1) At the top of the file sobolrsg.cpp a variable called
>  > AltPrimitivePolynomials is set up. This variable seems to just
>  > re-order some of the primitive polynomials (as compared to the order
>  > in primitivepolynomials.c). Is there a theoretical reason for doing
>  > this, i.e. does it improve some property of the numbers generated? I
>  > haven't seen this step described in any of the literature I have read
>  > on the method (e.g. Jäckel's book).
>  >
>  > 2) Do you have any feel for which method for initialising the free
>  > direction integers provides the best results?
>
>  On Mar 23, 2008, at 6:18 PM, Mark joshi wrote:
>
>  > There are two popular orderings for the polynomials in the literature.
>  > We need a variable to switch between the two.
>  >
>  > I reckon that JoeKuoD7 is the best.
>
>  [ Administrator note: to help keeping threads organized, when replying to a post, please use an actual "reply" and keep the subject intact.
>  Thanks, Luigi ]
>
>
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--
Quant Job Interview Questions and Answers coming very soon...

 www.markjoshi.com

Assoc Prof Mark Joshi
Centre for Actuarial Studies
University of Melbourne
My website is www.markjoshi.com

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