Lecture 16. D) Conjugate Priors
You may have noticed that we started out with a Beta prior, and ended with a Beta posterior; the only difference between the distributions were the parameters.
In this case, we say that the Beta distribution is a conjugate prior with a Bernoulli likelihood, i.e., when using the Bernoulli likelihood, starting with a Beta prior will leads us to a Beta posterior. This is extremely convenient, since it allows us to simply update distribution parameters.
When this does not hold, one has to keep track of the whole posterior distribution, which typically gets more and more complicated as more data is fed into it. You can find a list of conjugate priors here.