Author: Smith
Year: 1992
- goal find the posterior, from data
$x$ and a prior distro$p(\theta)$ : $$ p(\theta | x) = p(\theta; x) p(\theta) / \int p(\theta, x)p(\theta) d\theta $$ - so the goal is to generate samples from a distribution
$h(\theta)$ continuous wrt to$g(\theta)$ - Proposes methods to generates samples from
$h(\theta)$ that is a normalized density$h = f / \int f$ with samples of$g$ and the functionnal form of$f$ - Introduces the rejection method and the weighted bootstrap
- For the Bayes theorem we have
$f_x(\theta) = p(\theta; x) p(\theta)$ and the sampled distribution is precisely the posterior$p(\theta | x)$ - Illustrative example with a sum of binomial distribution