I want to calculate the joint probabilities P(X,Y), where X and Y are both categorical variables with 7 and 6 categories each. Given the conditional probabilities P(X|Y), is it possible to calculate the joint probabilities P(X,Y)?
If it is not possible from just P(X|Y), would it be possible if I had both P(X|Y) and P(Y|X)? As I have a model for estimating the conditional probabilities, but not the joint probabilities. And how would this exactly be done? I learnt how to do this in the case that both X and Y are binary variables, from this question,
but I am not quite sure how to extend this to the multinomial variables case. Thank you so much!!