I'm trying to figure out how to deal with rational inference in movie watching using probability theory.
So, for instance, I'm thinking of a situation like the one in the link below (which is my own example). Here, a viewer has some information about a scene: there's a woman on the beach, she's with her friend, and she's wearing a fine dress. The viewer sees the woman from behind, so the viewer does not know whether the woman is happy or not – but the viewer is curious and wants to predict the probability that the woman is happy. I've tried to formalize the situation:
I'm not sure the second equation in the link is meaningful... I want to have an equation for exact probability/inference of such a situation given a situation where the viewer has all the data it needs. Is it possible to rewrite the equation so that only simple conditional probabilties are in the equation? I mean, the equation as it stands is pretty ugly!
I'm not sure how to go about making it simpler. Obviously, it depends on the knowledge the viewer has of the different conditional probabilities.