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Simulation for Data Science with R by Matthias Templ

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Chapter 5. Monte Carlo Methods for Optimization Problems

Function optimization was applied in Chapter 4, Simulation of Random Numbers to find the maximum of a normal density divided by a Cauchy density as well as to find the extreme of a Beta distribution function. In this chapter, we will concentrate on two-dimensional problems and note that the mentioned methods can be extended to multi-dimensional problems. To convey a feeling of how optimization methods work, we start with a story set in the Austrian Alps.

When I wrote these lines we suddenly had foggy weather in Austria. And I imagined the scenario of a guy from Australia visiting Austria. Note that kangaroos exist only in the zoo in Austria, and that 70 percent of Austria is covered by mountains ...

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