Lecture 14: Why simulate? Generating random variables as first step. The built-in R commands: rnorm, runif, etc.; sample. Some uses of sampling: permutation tests; bootstrap standard errors and confidence intervals. Transforming uniformly-distributed random variables into other distributions: the quantile trick; the rejection method; illustration of the rejection method. Understanding pseudo-random number generators: irrational rotations; the Arnold cat map as a toy example of an unstable dynamical system; illustrations of the Arnold cat map. Controlling the random number seed.
Readings: Matloff, chapter 8; The R Cookbook, chapter 8
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