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MathGroup Archive 2007

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Adaptive Monte Carlo integration algorithm(s) in Mathematica6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75654] Adaptive Monte Carlo integration algorithm(s) in Mathematica6
  • From: Denis <denis.che at gmail.com>
  • Date: Tue, 8 May 2007 05:44:54 -0400 (EDT)

I'm happy with Mathematica 5.2 in most respects, except it doesn't
offer any *adaptive* Monte Carlo methods for multi-dimensional
integration.  Simple pseudo-random MonteCarlo and the non-adaptive
quasi-Monte Carlo are no match for the 6-dimensional integrals I need
to calculate.  Right now, as a way around that shortcoming, I am using
a third-party C code for LePage's VEGAS algorithm and run it in
Mathematica courtesy of MathLink.  It seems to work quite alright.

Now that Mathematica6 seems to offer adaptive Monte Carlo natively
within NIntegrate, my question is - which algorithm(s)?  I would like
to know whether Mathematica implemented their own version of VEGAS or
perhaps some other adaptive Monte Carlo algorithm...  Does anyone know
any specifics about this?

Thanks,
Denis


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