Let \(f\left(x\right)\) be a density and \(\pi\left(x\right)\) be a function satisfying \(0\leq\pi\left(x\right)\leq1\). In other words, \(\pi\left(x\right)\) is a probability for every \(x\). Then \(g\left(x\right)\propto f\left(x\right)\pi\left(x\right)\) is density, since \(\rho=\int f\left(x\right)\pi\left(x\right)dx<1\). This is an example of a , a class of models introduced by Rao (1965). Since \(p\left(x\right)\) is a probability, we can call this a . This note views rejection sampling (Neumann 1951) as sampling from a particular sort of probability weighted density.

Continue reading

Author's picture

Jonas Moss

Meta-contrarian statistician who wants to save science.

Ph.d. student in statistics, Universitas Osloensis

Oslo in Norway