Conjugate Priors

Introduction
Conjugate prior is a relatively well understood concept. Usually it comes from some kind of table, which tells you what kind of parameterized prior distributions you should use given the specific observation models. For example, if you have a Bernoulli or Binomial distribution with the probability of success as the unknown parameter, you should use a Beta distribution to model the unknown parameter; if you have a Poisson distributed observation with and unknown rate, then you should use Gamma distribution for that rate; a normal distribution with an unknown mean should have the mean modeled as normal too, but with a known mean and unknown covariance structure should have the covariance modeled by Wishart or inverse Wishart distributions, etc.