Basic sampling algorithms

We start our study of sampling algorithms by looking at some basic algorithms that can be used as subroutines in more advanced schemes. In all the algorithms from this book, we assume that we can generate random numbers uniformly from the interval [0,1]. The problem of generating random numbers on a computer is complex and vast. In most cases, random numbers will be generated by a deterministic algorithm, and they are called pseudo-random numbers. They are not random, but their distribution and properties are close enough to a real random generator that they can be used as real random numbers. Pseudo-random number generators are usually based on the estimation of chaotic functions that are extremely sensitive to their initial conditions, which are called the seed. Changing the value can generate a completely different sequence of numbers, even if the seed value is just a little bit different from the previous one. Nowadays, we also have electronic devices that can...