Introduction to Monte Carlo Methods

In this introductory chapter, we relate a short history of the Monte Carlo method and mention some of its uses. We illustrate the method by working through the Buffon needle problem for estimating \(\pi \) and show how to use histograms and sample paths to analyze the results. We will be using the computer language Python in programs to explain and demonstrate the concepts we cover throughout. Also in this chapter, we cover the basic concepts of probability theory that we will need throughout the book. This includes events, random variables both discrete and continuous, densities and cumulative distribution functions, expected values, the mean and variance of a distribution, conditional probability, and joint distributions.