Graphical Models:  Assignment 3
Due February 13, 2017

1. If Josin Stalif (dictator of Depravia) has the goal of becoming a world power, he may be planning to invade Impestuostria and he probably is developing nuclear weapons.  If he is developing nuclear weapons, he may try to steal nuclear materials and will probably buy reactors from first-world countries.  If he is planning to invade Impestuostria, Rechtian intelligence will probably see a troop buildup near the demilitarized zone.  A troop buildup could also occur as part of a routine training exercise, but the message traffic received by Rechtian intelligence would probably be different for exercise versus invasion.
1. Develop a Bayesian network structure (nodes, arcs and states) to infer Stalif's intentions. Use Bayesian network software to draw your network.
2. Explain your network.  Describe your nodes, states, and arcs, and explain why you chose the structure you did.
3. Enter local probability distributions for your Bayesian network.  Explain your distributions.
4. Consider two qualitatively different scenarios: (1) Rechtian intelligence sees a troop buildup and message traffic looks like an exercise; (2) Rechtian intelligence sees a troop buildup, message traffic does not look like an exercise, and Stalif has initiated a contract to buy a nuclear reactor from the country of Appesia. Compare the prior probability that Stalif has the goal of becoming a world power, and the posterior probabilities under the two different scenarios.  Comment.
1. Consider a noisy-OR model with k causes C1, ..., Ck of an effect E.  Assume that C1, ..., Ck are independent a priori.  Show that conditional on E = 0 (the effect is false), the causes C1, ..., Ck remain independent.