I am looking into influence diagrams and ways to simplify them. I noticed that to simplify the diagram, sometimes an arc between two chance nodes can change direction (in other words, it can go inversely, as long as they do not create a cycle).
I am not sure I’ve totally understand this, I know by using the conditional probability this can be explained, but chronologically I still cannot understand this. Although it is said that the arc into chance nodes only represent relevance rather than time sequence, I still think they should be somehow ordered. Can someone explain this?
I guess this is a dumb question that no one would like to answer, but I will just share my thought in this week.
I think the arc should not be considered as a ”dependent” sign, saying dependent always gives one a feeling of one thing is caused by another, however this is not how things worked. If we draw a Venn diagram of two dependent event, we will see there is certainly a common space between them, this is where they are “relevent”. Knowing one event will give some information on the common information, and thus will give information to another event, and this works in another direction. This is what the arc stands for.
So whenever two chance nodes are linked by an arc, it could be considered that they must have a “common space”, and knowing one will sure give “hint” to another, this works immediately and nor influenced by time.