Assume the Bayesian belief network for the diagnosis of car\'s electrical system
ID: 3251420 • Letter: A
Question
Assume the Bayesian belief network for the diagnosis of car's electrical system. Assume that all variables in the network are binary with True and False values. a. The belief network structure encodes conditional and marginal independences in graphical terms. Give at least three examples of conditional and one example of marginal independences encoded in the network structure. b. Assume that all variables in the network are binary (have two possible values). What is the total number of probabilities needed to define the full joint distribution? What is the number of free parameters? c. Give the expression for the full joint probability over variables using the Bayesian belief network and its parameters. Assume we are interested in calculating the joint probability for: Battery = T, Radio = F, Light = T, Ignition = T, Gas = T, EngineStarts = F, Carmoves = F.Explanation / Answer
Ans:a)Radio,lights and ignition depends on the functioning of the battery,if battery is working,only then these three will work,but 3 of them are mutually independent.(Conditional independent)
The Gas is marginally independent of all.
b)We need 7 probabilities to define the full joint distribution.
number of free parameters =2
c) Radio will work if battery is working so P(Radio works/Battery working)
Similarly,P(light works/Battery working)
P(Ignition works/Battery working)
P(Engine starts/(ignition works and Gas)
P(Car moves/engine starts)