Monte Carlo methods Week 2 , Simulation

Simulation, in this Monte Carlo course, will mean direct simulation. That means producing random objects according to some description. This was supposed to be almost the opposite of Monte Carlo, where the main activity is finding ways to “cheat” – to find different random variables with the same expectation value. This chapter is here for three reasons. One is that the moderately complex random objects here are great examples of things to do “Monte Carlo” tricks on – variance reduction and so on. Another is that there are interesting tricks already here that people doing computational probability (or computational stochastics use all the time. The final reason is possibly perverse pedagogical principle, the primacy of programming in the present applied mathematics paradigm. In other words, you don’t do applied mathematics in the 21-st century without computing. A class in applied mathematics has to have algorithms and programs. Simulation is a setting with mostly simple math where it is easy to do some more serious programming.