Design of Bayesian networks: Understanding the difference between “States” and “Nodes”

Question

I'm designing a small Bayesian Network using the program "Hugin Lite". The problem is that I have difficulty understanding the difference between "Nodes"(visual circles) and "States"(witch are the "fields" of a node).

I will write an example where it is clear,and another which I can't understand.

The example I understand:
There are two women (W1 and W2) and one men (M).
M get a child with W1. Child's name is: C1
Then M get a child with W2. Child's name is: C2

The resulting network is:

The four possibles STATES of every Node (W1,W2,M,C1,C2) are:

• AA: the person has two genes "A"
• Aa/aA: the person has one gene "A" and one gene "a"
• aa: the person has two genes "a"

Now the example that I can't understand:

The data given:

• Total(authorized or not) of payments while a person is in a foreign country (travelling): 5% (of course the 95% of transactions are transactions made in the home country)
• NOT AUTHORIZED payments while TRAVELLING: 1%
• NOT AUTHORIZED payments while in HOME COUNTRY: 0,2%
• NOT AUTHORIZED payments while in HOME COUNTRY and to a FOREIGN COMPANY: 10%
• AUTHORIZED payments while in HOME COUNTRY and to a FOREIGN COMPANY: 1%
• TOTAL (authorized of not authorized) payments while TRAVELLING and to a FOREIGN country: 90%

What I've drawn is the following.

But I'm not sure if it's correct or not. What do you think? Then I'm supposed to fulfill a "probability table" for each node. But what should I write?

Probability table:

Any hint about the network correctness and how to fullfill the table is really appreciated.

Answer 1

This is homework so I don't want to just tell you the answer. Instead, I'll make an observation, and ask a few questions. The observation is that you want your arrows goig from cause to effect.

So. Is the payment authorization status a/the cause of the location? Or is the location a/the cause of the payment authorization?

Also, do you really need four variables for each of travelling, home, foreign, and local? Or might some smaller number of variables suffice?

Answer 2

Nodes are Random Variables (RV), that is is "things" that can have different states thus with certain levels of uncertainty therefore you assign probabilities to those states. So for example if you talk of RV of Person it could have different states such as [Man or Woman] with their corresponding probabilities, if you want to relate it to another RV Credit Worthiness [Good,Bad] then you can "marry" Person and Credit Worthiness to have a combination of both RV and the combination of states.