# Posterior probability

(Redirected from Posterior distribution)
${\displaystyle f_{X\mid Y=y}(x)={f_{X}(x)L_{X\mid Y=y}(x) \over {\int _{-\infty }^{\infty }f_{X}(x)L_{X\mid Y=y}(x)\,dx}}}$
• ${\displaystyle f_{X}(x)}$ is the prior density of X,
• ${\displaystyle L_{X\mid Y=y}(x)=f_{Y\mid X=x}(y)}$ is the likelihood function as a function of x,
• ${\displaystyle \int _{-\infty }^{\infty }f_{X}(x)L_{X\mid Y=y}(x)\,dx}$ is the normalizing constant, and
• ${\displaystyle f_{X\mid Y=y}(x)}$ is the posterior density of X given the data Y = y.