Understanding Joint Probability Model

[pamparana]

Hello everyone,

I am trying to understand a paper and am stuck at one place.

The statement says something as follows:

Say we have a, b, c and d which are random variables generated by some model. This leads to the following joint probability model:

p(a, b, c, d) = p(a|b)p(b|c,d)p(c)p(d)

I do not understand the RHS of the equation at all? What is it saying and quite confused as to how it is derived?

Would be very grateful for any help you can give me.

Thanks,
Luca

 

[SW VandeCarr]

Say we have a, b, c and d which are random variables generated by some model. This leads to the following joint probability model:

p(a, b, c, d) = p(a|b)p(b|c,d)p(c)p(d)

I do not understand the RHS of the equation at all? What is it saying and quite confused as to how it is derived?
Luca

probability of (a conditional on b) times probability of (b conditional on c,d) times the joint probability of c and d.

You say "some model" If they provided no further information, take it as a given. Conditioning on c,d and multiplying by the joint probability are two different operations.

EDIT: In calculating for conditioning on two or more variables, you try to marginalize one of the variables:

P(A|B,C)=P(A,B,C)/P(B,C)=P(A,B,C)/P(B)P(C|B)=P(C|AB)P(A,B)/P(B)P(C|B)=P(A)P(B|A)P(C|AB)/P(B)PC|B).

This is less complicated then your example with four variables, but it shows the concept of marginalization of P(B) and P(C).