We say that $\pi(\theta)$ is a conjugate prior for $f(\theta \ |\ x)$ if the posterior, $\pi(\theta \ | \ x) \propto \pi(\theta) \ f(\theta \ | \ x )$, is from the same model family as the prior. Common conjugate families include - [[beta-binomial conjugate]] - [[normal-normal conjugate]] - [[inverse gamma-normal conjugate]] - [[gamma-Poisson conjugate]] - [[gamma-exponential conjugate]]