Attempting to understand Exercise 20 (pdf page 44) in the paper: (Warning: large paper; small exercise)
Bayesian Reasoning and Machine Learning
The party animal problem corresponds to the network in g(3.14). The boss is angry and the worker has a headache - what is the probability the worker has been to a party?
When set to 1 the statements are true: P = Been to Party, H = Got a Headache, D = Demotivated at work, U = Underperform at work, A =Boss Angry. Shaded variables (A, H) are observed in the true state.
$\begin{matrix} & & D \\ & & \downarrow \\ P & \rightarrow & U \\ \downarrow & & \downarrow \\ (H) & & (A)\end{matrix} $
I would like to solve the following:
- Prove that p(P|H,A ) = a*p(P,H,A) where a is a constant.
- Expand p(P, H, A) by marginalizing over the variables U and D.
- how to compute 'a'
Any help is greatly appreciated.
Thank You.