Mathematical Sciences: Random Variables and Computers

随机变量的生成和测试为蒙特卡罗模拟提供了一些最广泛使用的方法。针对新型的计算机体系结构，已经开发了几种新的方法，其中最著名的是借减法，它速度非常快，需要很少的内存位置，具有极长的周期和可证明的一致性。目前的努力方向是利用大规模并行系统、新的大容量存储设备和其他超级计算机特性的方法，以便统计计算软件能够跟上并利用硬件的显著进步。由于基础模型的不确定性或复杂性，许多计算机模拟研究要求在不同的点上随机输入。“伪随机”数的构造可以足够复杂，可以为自然过程中的真实随机观测提供可行的替代品。同时，这些生成的数字很容易获得，并且可以在需要时精确地复制用于测试目的或比较两种不同的计算方法来解决极其庞大和复杂的数学问题。

The generating and testing of random variables has provided some of the most widely used methods for Monte Carlo simulation. Several new methods have been developed for new kinds of computer architectures, notably the subtract-with-borrow method that is very fast, requires few memory locations, has extremely long periods and provable uniformity. Current efforts are directed toward methods that will take advantage of massively parallel systems, new mass storage devices and other supercomputer features so that software for statistical computing can keep up with and take advantage of the remarkable advances in hardware. Many computer simulation studies call for random input at various point because of uncertainties or complexities of the underlying models. The construction of "pseudo-random" numbers can be sufficiently sophisticated to give workable substitutes for true random observations from a natural process. At the same time these generated numbers are readily available and can, when needed be reproduced exactly for testing purposes or to compare two different computing approaches to the solution of extremely large and complicated mathematical problems.