I've the following joint distribution:
$p(x1, x2, y1, y2) = p(x1, x2)p(y1|x1)p(y2|x2)$
And I'm told that it implies the following Markov chain:
$Y1 → X1 → X2 → Y2$
I cant' see the equality between the two. Clearly, if the given markov chain is correct then joint distribution can be written as follows:
$p(x1, x2, y1, y2) = p(y1)p(x1|y1)p(x2|x1)p(y2|x2)$
So how are those 2 joint distributions equal ?