Using Quasi–Monte Carlo in Practice
In the preceding chapter, we presented several constructions that can be used for quasi–Monte Carlo sampling and discussed how to assess their quality. In this chapter, we focus on issues that arise when applying quasi–Monte Carlo methods in practice. We first discuss randomized quasi–Monte Carlo, which, as we mentioned at the end of the previous chapter, is an essential tool to make low-discrepancy sampling applicable in practice. In Sect. 6.3, we discuss ANOVA decompositions, which have been very useful for understanding the success of quasi–Monte Carlo methods in practice. We discuss in Sect. 6.4 the use of quasi–Monte Carlo sampling in simulation studies and how it can be combined with other variance reduction techniques. We conclude in Sect. 6.5 with a short discussion of different issues and suggestions that might be helpful to practitioners.
We include an appendix to this chapter, where we briefly discuss the concept of tractability and related results that have had a great impact on the construction of low-discrepancy point sets over the last few years. This area of study has connections with ANOVA decompositions, which is why we chose to present it in this chapter rather than the previous one, but it does not exactly fit with the more simulation-oriented issues discussed in the rest of the chapter, which is why we put it in an appendix. This chapter does not focus on specific applications. The next chapter will discuss the use of quasi–Monte Carlo sampling in finance, which is probably the most well-known application for these methods. Another area where quasi–Monte Carlo has been quite successful is computer graphics [213, 460]. The survey  by Owen describes quasi–Monte Carlo sampling for people working in that area.
KeywordsMonte Carlo Monte Carlo Sampling Monte Carlo Estimator Brownian Bridge Quantile Estimator
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