Chapter 8 Advanced Monte Carlo Methods
Learning Objectives
- To be able to explain and apply the basic principles of bootstrap sampling
- To be able to apply variance reduction techniques to simulation experiments
- To be able to apply the main techniques recommended for generating multi-variate random variables
- To be able to apply Markov Chain Monte Carlo techniques to the generation of random variables
This chapter builds on the methods presented in Appendix A, Chapter 2, and Chapter 3 to present advanced Monte Carlo techniques that are often applied in practice. The chapter begins with a discussion of bootstrap sampling methods. Bootstrap sampling was popularized by (B. Efron and Tibshirani 1994) and remains a practical and useful technique that every simulation practitioner should be able understand and apply. Then, the chapter presents more details on the application of variance reduction techniques (VRTs). While some of the facilities of the KSL for the application of two variance reduction techniques (common random numbers and antithetic variates) have already been presented, this chapter will provide more details on the theory of those and other variance reduction techniques. In addition, the application of the techniques will be illustrated via some simple examples. As discussed in Chapter 2, the KSL has exceptional functionality for the generation from uni-variate distributions. In this chapter, the capabilities for generating from multi-variate distributions will be reviewed and illustrated via some simple examples. Finally, a brief discussion of the important topic of Markov Chain Monte Carlo (MCMC) will be provided. Then, the KSL’s framework for performing MCMC will be illustrated. This chapter assumes that the reader is familiar with the general concepts presented in Appendix A, Chapter 2, and Chapter 3.
NOTE!
This chapter provides example code of using the KSL to implement advanced Monte Carlo techniques. 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.