Working with Randomness and Probability

In this chapter, we will discuss randomness and probability. We will start by briefly exploring the fundamentals of probability by selecting elements from a set of data. Then, we will learn how to generate (pseudo) random numbers using Python and NumPy, and how to generate samples according to a specific probability distribution. We will conclude the chapter by looking at a number of advanced topics covering random processes and Bayesian techniques and using Markov Chain Monte Carlo (MCMC) methods to estimate the parameters of a simple model.

Probability is a quantification of the likelihood of a specific event occurring. We use probabilities intuitively all of the time, although sometimes the formal theory can be quite counterintuitive. Probability theory aims to describe the behavior of random variables whose value is not known, but where the probabilities of the value of this random variable take some (range of) values that are known. These...