1. The problem statement, all variables and given/known data Hi, so I am having trouble understanding the steps to get to certain densities. For example, suppose i have data y1,...,yJ ~ Binomial (nj,θj) We also have that θj ~ Beta (α,β) Now our joint posterior is: p(β,α,θ|y) ~ p(α,β) ∏ ([itex]\Gamma[/itex](α+β) / [itex]\Gamma[/itex](α)[itex]\Gamma[/itex](β)) θjα+yj-1(1-θj)β-1+nj-yj Next, we find the posterior of θ given (α,β,y), the "joint density". I do not understand this step. Here is what it is suppose to be: p(θ|α,β,y)= ∏ ([itex]\Gamma[/itex](α+β+nj) / [itex]\Gamma[/itex](α+yj)[itex]\Gamma[/itex](β+nj-yJ)) θjα+yj-1(1-θj)β-1+nj-yj How did they get this? In my class and from sources I have read it says you can obtain this by "dropping the terms that are not dependent on θ"... but I do not see where the nj and + yj, etc. came from. After this step we wish to find the marginal posterior of (α,β), p(α,β|y) ~ p(β,α,θ|y)/p(θ|α,β,y. Is there another way to do this as well? I know it can also be written as p(α,β|y)~ g(α,β) ∏ f(yj|α,β). But then, if done this way, what is f(yj|α,β). In another example: http://www-stat.wharton.upenn.edu/~edgeorge/Research_papers/GZpriors.pdf On the 6th page, it says, integrating out θ1,...,θp, we get... How did they integrate out exactly? I realize these are questions I should know from calculus but I just don't understand the steps to getting these results. Any help is appreciated!