Monte Carlo Methods

This tutorial describes numerical methods that are known as Monte Carlo methods. It starts with a basic description of the principles of Monte Carlo methods. It then discusses four individual Monte Carlo methods, describing each individual method and illustrating their use in calculating an integral. These four methods have been implemented in my example program 8.2, and the results from these are used in my discussion on each method. This discussion looks at the principles behind each method. It also looks at the approximation error for each method and compares each different method’s approximation accuracy. After this, the tutorial discusses how Monte Carlo methods can be used for many different types of problem, that are often not so obviously suitable to Monte Carlo methods. We then discuss the reasons why Monte Carlo is used, attempting to illustrate the advantages of this group of methods. Finally, I discuss how Monte Carlo methods relate to the field of Computer Vision and give examples of Computer Vision applications that use some form of Monte Carlo methods. Note that the appendix includes a basic mathematics overview, the program code and results that are refered to in section 3 and some focus questions involving Monte Carlo methods. This tutorial does contain a moderate content of mathematical and statistical concepts and syntax. The basic mathematics overview is an attempt to describe some of the more familiar concepts and syntax in relation to this tutorial and thus a quick initial review of this section may improve the understandability and clarity of it.