Normaly, if i wanted to do some monte-carlo simulation, i'd generate a bunch of variates with a given volatility and correlation. I would generate them by taking a choleski decomposition of the desired covariance matrix, and multiply that by some mean zero standard dev one random numbers that i had generated by box-muellernow i understand that sobol sequences "fill in" the unit hyper cube more efficiently than something like box-mueller, but my instincts tellme that i will violate "some assumption" of monte-carlo by simply taking a sobol sequence and multiplying it by the cholseki decomp of the covariance matrix any insight [as to how to work around what i might mistakenly perceive as a problem] gratefully apreciated

???Box-Muller transform is to get two normal random variables out of two uniform random numbers.Sobol sequence is to get bunch of uniform random numbers. I don't see any conflicts. When you get two numbers out of Sobol sequence and put them intoBox-Muller transform, you still get two normal random variables (pseudo random variables, to beaccurate). When you get a standard normal random vector (mean zero, uncorrelated, unit variance), you multiply sqrt of your cov matrix (from Cholesky) to get a correlated normal random vector asdesigned.You're not using this for supply/demand model for power, are you? (just joking).

Box-Muller distorts Sobol sequencies. You should use some other transform e.g. B. Moro

Like in Mike Staunton's article?What happens if I do rejection on Box-Muller as in Numerical Recipe?This is usually twice faster than plain Box-Muller (I've tested this with a mersenne twister implemented byboost). Also hard to see if there's a systematic bias. (no?)PS: Actually, NAG uses plain Box-Muller on Sobol, so I shouldn't rely on this.

Actually one schould not use Sobol sequences together with Box-Muller. The reason is that one loses the good distribution properties of the sobol sequences. In all our investigations it was the best use the inversion method, with some approximation for the inverse distribution function. These approximations are at least for the normal distribution rather good. The problem of using Box-Muller together with e.g. Mersenne Twister is much lower. To even improve the convergence, when using sobol numbers, one can use other decompositions of the covariance matrix such as singular value decomposition or a brownian bridge approach, whereas we never saw significant improvemnts whenever we combined Monte Carlo numbers (Mersenne Twister, Linear congruential methods) with SVD or BB.

there's a section in PJ's book in this.If numbers are truly random (which is of course impossible in a computer) it makes no difference what method of conversion to normals is used.Brownian bridge, SVD, etc have no theoretical impact either. If we use pseudo-randoms which are effectively truly random then we are in the same situation.If we are low-discrepancy eg Sobol, then we need to be much more careful. Anything that scrambles them is bad so Box-Muller should be avoided. Rejection methods require extra variates so should be avoided too. SVD and brownian bridge make a difference as they cause the low dimensions which are better to have more impact. MJps we need to get this stuff under FAQs as it must be the 4th time I've answered this question