Chapter 4. Simulation of Random Numbers

Can you imagine a statistical simulation to evaluate and compare methods without generating random numbers? Can you imagine a Bayesian approach without drawing random numbers from predictive or prior distributions? Can you imagine any game of chance without the concept of randomness? Can you imagine a world without randomness?

Generally speaking, the statistics and probability theory is based on abstract concepts of probability space and random numbers. An elegant mathematical theory has been developed, which takes its starting point from random numbers.

Specially applied research areas such as computational statistics, data science, and statistical simulation employ the concept of random numbers. Hereby, often a large number of independent and identically distributed (i.i.d) random numbers are generated/needed, especially for simulation purposes.

However, in computer applications, surprisingly the random numbers are mostly simulated with deterministic...