Dear All, I am a starter to machine learning and i am currently confused about the following problem: what is the result of P(X|Y)P(Y|Z)? In my book, it is written to be P(X|Z). But I don't think it is correct since P(X|Z)= P(X|Y,Z)P(Y|Z) But clearly P(X|Y)=/= P(X|Y,Z) Assuming all Events are not independent. I have simplified the problem in the above equation. The true equation is p(w|x,t,α,β)proportional to p(t|x,w,β)p(w|α) from pattern recognition and machine learning written by christopher m. bishop. Any helps and ideas will be very appreciated.