Monte Carlo

December 17, 2011 1:15 PM

The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF). -N. Metropolis

Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).
posted by JoeXIII007 (13 comments total)

Approximating π by the Monte Carlo method is a fun little programming exercise.
posted by Monday, stony Monday at 1:21 PM on December 17, 2011

Heh. When I was writing my dissertation the literature was small enough that I was reading papers by Metropolis and reports on some of the work he and his colleagues did (modeling neutron fluxes in atomic reactors and/or explosions, iirc. Don't think I ended up citing anything that old.
posted by zomg at 1:35 PM on December 17, 2011

So where's our statistical sampling non-proliferation treaty?
posted by jamjam at 1:49 PM on December 17, 2011 [1 favorite]

I have some neat R demonstrations that show various (MC)MC techniques in action, step by step. I've been meaning to put these on the web, but translating them from R to something more web friendly would be nontrivial...
posted by Philosopher Dirtbike at 1:49 PM on December 17, 2011 [1 favorite]

The state of MCMC software makes me sad. Academics who come up with fancy improvements to samplers generally don't have the resources or incentives (or desire) to make them into usable products. SAS/Stata should be figuring this out and putting their considerable implementation expertise to bear.
posted by a robot made out of meat at 2:31 PM on December 17, 2011

The first electronic computer was 1943
posted by BigCalm at 3:00 PM on December 17, 2011

This is cool
posted by DoctorFedora at 4:15 PM on December 17, 2011

don't forget the control variate method
posted by cupcake1337 at 4:44 PM on December 17, 2011 [2 favorites]

Want to be able to do criticality calculations to ensure your highly enriched uranium Christmas ornaments won't go critical if you drop them in the tree's water? Need to figure out how thick your walls need to be so that your garage-based cobalt 60 irradiator won't harm the family?

Willing to promise the US government you won't attempt to build nuclear weapons with it?

Apply to get Monte Carlo N–Particle Transport Code System sent to you via the US Mail through RSICC. And in approximately 8.64 × 10^13 shakes of a lamb's tail, you'll have your own fully operational Monte Carlo radiation transport code.
posted by pseudonick at 5:49 PM on December 17, 2011

MCNP is free, but you'll need to come up with some reasonably sounding justification if you want it shipped to you. Ask for the compiled executable instead of the source package for better odds.

You're probably out of luck if you aren't an American citizen.
posted by pseudonick at 6:01 PM on December 17, 2011

1945?
How about 1941?
Forget about this guy?
posted by 360 at 6:24 PM on December 17, 2011

don't forget the control variate method

That is insanely brilliant. Exactly the kind of outside-the-box thinking that I just can't do.
posted by benito.strauss at 8:46 PM on December 17, 2011

Philosopher Dirtbike - Throw them up on Github as R gists as they are! I'd love to see them!
posted by stratastar at 5:13 PM on December 18, 2011