I'm trying to find the expression for posterior probability $$f_R(r|z)=\frac{f_Z(z|r)f_R(r)}{f_Z(z)}$$ where Z, R and W are random variables, R and W not necessarily independent and Z = R + W.
Since W = Z - R, is it legit to conclude :
$$f_Z(z|r) = f_W(z - r|r)?$$
My gut feeling is yes but I can't justify this...
Also, does W and R being independent or not affect the conclusion?
Please provide theory to back up your thoughts and thanks for anyone to help me!
Update: 22:59 07-Dec-2019
Answer provided in the comment, conclude later...