Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am a quantum physicist who needs a practical help from mathematicians.

The physical problem that I have can be reduced to the following mathematical problem:

Assume that we have two correlated variables a and b. Assume that we know all conditional probabilities

P(a|b), P(b|a)

for all possible values of the variables a and b.

What I want to know are all joint probabilities P(a,b). However, a priori they are not given. I want to ask the following:

What is the best I can conclude about P(a,b) from knowledge of P(a|b), P(b|a)?

Are there special cases (except the trivial case in which a and b are independent) in which P(a,b) can be determined uniquely?

Any further suggestions?

Thank you in advance!

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# Joint probability from conditional probability?

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