Inverse Transform Sampler
A method to draw samples of some univariate random variable \(X\), assuming we know the inverse of its cumulative distribution function \(F_X\), \(F^{-1}_X\).
U = Uniform[0,1] X = InverseCDF(U)
Thoughts
- Proofs on Wikipedia, Murphy's PML book V2 and the "Non-uniform Random Variate Generation" textbook seem too vague, Jimmy Olsson spent a fair bit of time proving this rigorously, so need to check where the mismatch is.