Lecture Notes in Computer Science vol:3984 pages:780-788
Computational Science and Its Applications - ICCS 2006 location:Glasgow, United Kingdom date:May 8-11, 2006
To use quasi-Monte Carlo methods, the integral is usually first (implicitly) transformed to the unit cube. Integrals weighted with the multivariate normal density are usually transformed to the unit cube with the inverse of the multivariate normal cumulative distribution function. However, other transformations are possible, amongst which the transformation by Box and Muller. The danger in using a non-separable transformation is that it might break the low discrepancy structure which makes quasi-Monte Carlo converge faster than regular Monte Carlo. We examine several transformations visually, theoretically and practically and show that it is sometimes preferable to use other transformations than the inverse cumulative distribution function.