## Belief Propagation

** Published:**

## Introduction

Let $(\Omega^n, \mathscr A^n, \mu)$ be a probability space such that $\mu \in \mathcal P$ where $\mathcal P$ is a family of probability measures defines on $\mathscr A^n$. Also let $X = (X_1, \cdots, X_n)$ be a random vector so that $X_i: \Omega \to \mathbb R$ is a measurable function for all $i = [n]$. Then the marginal probability of $X$ is defines as