Bayesian Network Design

Question

I have a basic question about Bayesian networks.

• Suppose we have an engine that with 1/3 probability may stop working. I will call this variable ENGINE.
• If it stops working, then your car is not working. If the engine is running, then your car will run 99% of the time. I will call it CAR.
• Now, if your car is old (OLD), instead of not working 1/3 of the time, your engine will stop working 1/2 of the time.

I am asked to first design the network, and then assign all the conditional probabilities associated with the table.

I would say that the scheme of this network will be similar to

OLD -> ENGINE -> CAR 

Now for conditional probability tables, I did the following:

 OLD |ENGINE ------------ True | 0.50 False | 0.33 

and

 ENGINE|CAR ------------ True | 0.99 False | 0.00 

Now I am having problems with how to determine OLD probabilities. From my point of view, the old one is not something that CAUSE has to do with ENGINE, I would say that this is more characteristic of it. Maybe there is another way to express this in a diagram? If the chart is really correct, how can I make the tables?

Answer 1

I think OLD is something like a parameter that is given from the outside world. Thus, this is not really a random variable and may not need to be part of your chart, depending on how her teacher sees her.

Answer 2

I think the problem here is not specific enough as to what the predicates CAR, OLD, and ENGINE mean.

I could name them: EngineWorks, CarOld, CarWorks

EngineWorks and CarOld are parents of CarWorks. I think we can agree that EngineWorking and CarOld are the direct causes of CarWorks, as described in your problem. I would also simulate CarOld as the parent of EngineWorks. I think CarOld -> EngineOld -> Engine is not working.

Now you have the problem of setting the desired probabilities on this graph. It should not be difficult.