Chapter 3 Monte Carlo Methods

Learning Objectives

• To be able to collect statistics using classes within the KSL
• To understand the basics of statistical computations supported by the KSL
• To be able to perform simple Monte Carlo simulation experiments using the KSL
• To review statistical concepts and apply them to the analysis of simple Monte Carlo simulation experiments
• To illustrate generating and collecting statistics for Monte Carlo simulation experiments

This chapter illustrates how to use the KSL for simple Monte-Carlo simulation experiments. The term Monte Carlo generally refers to the set of methods and techniques that estimate quantities by repeatedly sampling from models/equations represented in a computer. As such, this terminology is somewhat synonymous with computer simulation itself. The term Monte Carlo gets its origin from the Monte Carlo casino in the Principality of Monaco, where gambling and games of chance are well known. There is no one Monte Carlo method. Rather there is a collection of algorithms and techniques. In fact, the ideas of random number generation and random variate generation previously discussed form the foundation of Monte Carlo methods.

For the purposes of this chapter, we limit the term Monte Carlo methods to those techniques for generating and estimating the expected values of random variables, especially in regards to static simulation. In static simulation, the notion of time is relatively straightforward with respect to system dynamics. For a static simulation, time ‘ticks’ in a regular pattern and at each ‘tick’ the state of the system changes (new observations are produced).

A key requirement in performing a Monte Carlo simulation is the ability to collect and report statistics on observations generated by the simulation. The KSL supports the collection of statistics within the ksl.utilities.statistics package. Before proceeding with examples illustrating Monte Carlo methods, the following section overviews some of the statistical and reporting capabilities of the KSL.

NOTE! This chapter provides a series of example Kotlin code that illustrates the use of KSL constructs for Monte Carlo methods. The full source code of the examples can be found in the accompanying KSLExamples project associated with the KSL repository. The files for each example of this chapter can be found here.