# Designing bayesian networks

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### Question

I have a basic question about Bayesian networks.

1. Let's assume we have an engine, that with 1/3 probability can stop working. I'll call this variable ENGINE.
2. If it stops working, then your car doesn't work. If the engine is working, then your car will work 99% of the time. I'll call this one CAR.
3. 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'm being asked to first design the network and then assign all the conditional probabilities associated with the table.

I'd say the diagram of this network would be something like

``````OLD -> ENGINE -> CAR
``````

Now, for the conditional probabilities 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 trouble about how to define the probabilities of OLD. In my point of view, old is not something that has a CAUSE relationship with ENGINE, I'd say it is more a characteristic of it. Maybe there is a different way to express this in the diagram? If the diagram is indeed correct, how would I go to make the tables?

### Solution

I guess OLD is something like an parameter that is given from the outside world. Thus, it's not really a random variable and possibly should not be part of your diagram, depending on how your teacher sees it.

### OTHER TIPS

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

I might name them: EngineWorks, CarOld, CarWorks

EngineWorks and CarOld are the parents of CarWorks. I think we can agree that EngineWorking and the CarOld are direct causes of CarWorks as described in your problem. I would also model CarOld as a parent of EngineWorks. My thinking is that CarOld -> EngineOld -> Engine doesn't work.

Now you are left with the problem of fitting the desired probabilities to this graph. That should not be hard.