ABSTRACT
Fast computers have revolutionised statistics. The ease with which we can now optimise functions numerically, as described in Chapter 3, provides one primary illustration. Simulation provides another. Our aim in simulation is to mimic the probability rules of models and we typically do this by obtaining realisations of random variables. Thus the histogram in Figure 6.1, for example, summarises the results of 200 simulations of a random variable with a particular distribution. To obtain such results without a computer would be tedious. Early simulations for use in statistics were obtained using mechanical means, but only for the simplest situations. As we shall see shortly, simulation using a computer is extremely valuable. It releases us from the straight-jacket of relying on asymptotic procedures. Furthermore, using fast simulation procedures, Bayesians can now effectively fit highly complex models to data, a discovery which has changed the face of statistics, and which is the subject of the next chapter. Later in this chapter we shall discuss the various uses of simulated random variables, but before that we shall describe the essentials of how they are generated.
