TY - CHAP
TI - Do We Need Arbitrary Precision Random Variate Generators in Monte Carlo Simulation?
AB - Libraries for multiple-precision floating-point computations overcome the limitations of floating point numbers in single or double precision at the expense of longer running times. Extensions of such libraries now also provide random variate generators for this purpose. Knuth and Yao (1976) have shown that a remarkable simple algorithm by von Neumann (1951) is perfectly suited for sampling exponentially distributed random variates exactly. Here "exactly" means that each digit of the decimal representation follows the correct law. Even further the algorithm allows to represent random variates with infinite precision in programming languages with lazy evaluation as requested digits can be easily generated "on-the-fly". Karney (2013) has adapted this algorithm to sample from the normal distribution by means of a rejection method. Besides the pure aesthetic aspect of this beautiful algorithm one also may ask a practical question: Given the slower generation rate, is it worth the effort to use such multiple-precision random variates in Monte Carlo simulations? From a purely pragmatically point of view the answer would be no if we do not see any difference to ordinary random variates in double format. In this talk we want to estimate minimal sample sizes that allow to distinguish between random variates stored as floating point numbers of different precision by means of statistical tests.
AF - Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
PP - Leuven
PY - 2014-01-01
AU - Leydold, Josef
ER -