The Conjugate Beta Prior

Hello. I'm having a problem with trying to figure out this proof that shows the beta distribution is conjugate to the binomial distribution (picture attached). I understand it until the third row, but I got confused with this step from the third to the fourth row. I would appreciate a simple explanation. Thank you in advance.


1 Answer 1


To go from the third to fourth row just ignore factors that are constant with respect to $\pi$. That is, let



$$p(\pi|y)=k \cdot \pi^y (1-\pi)^{(n-y)}\pi^{(\alpha-1)}(1-\pi)^{(\beta-1)}$$


$$p(\pi|y) \propto \pi^y(1-\pi)^{(n-y)}\pi^{(\alpha-1)}(1-\pi)^{(\beta-1)}$$

The idea's to deal just with the kernel of the probability distribution, knowing you can always put the normalizing constant back in later.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.