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I am working on image processing and my probability theory knowledge is low. My question here is I am working with 2 variables X and Y which is dependent on each other. That is we can compute P(X|Y) or P(Y|X). The distribution of each is normal and X not equal to Y.

Baysian Network is more a directed relationship modeling, i.e only one what. If I did understand correctly than I can compute P(X|Y) but not P(Y|X). Is this correct?

My problem is as I stated above i want to model 2 variables that are dependent on each other. I read through Markov Random Fields but I am not sure if it can represent what I need. Please advice me of any possible representation (distribution) I can use to model the 2 variable. Thank you

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Since both variables are Gaussian, the natural model for their joint distribution is a multivariate Gaussian distribution.

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