Tweedie's Formula

Definition

The Tweedie’s formula provides a way to estimate the posterior mean: the conditional expectation of a random variable $x$ given an observation $y$ that is related to the $x$. $\mathbb{E}[x|y]=y+{\sigma }^2\nabla \ln p(y)$ where $y$ is an observed data, ${\sigma }^2$ is a variance of the noise, and $\nabla \ln p(y)$ is the Score Function functioning as a correction term in the formula.