Statistical relationship between the stages of a stochastic optimization problem What exactly do the "stages" of a stochastic program say about the statistical relationship between the problem variables?
From what I understand, the stages imply both an "ordering" and "grouping" of variables. What are the semantics of such designation of variables?
For example:

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*Is it correct to say that stages are a modeling assumption of the statistical relationship between the problem variables?

*What's the information theoretic nature of that relationship?

Example:
In a typical "two stage" (e.g. production) stochastic program one often distinguishes between:

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*"First-stage" decisions (variables)

*"Second-stage or "recourse" decisions (variables)

In terms of their statistical dependency or Bayesian relationship, is it correct to say that this simply states that:

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*1st stage variables are "realized" (decided) independently of 2nd stage variables

*The realization (decision) probabilities of 2nd stage variables depend on the realization of 1st stage ones?

Or is there anything deeper to it?

In case it helps, I found the following in our sibling SE.OR site:

Oe might confuse the notion of time periods and stages in stochastic programming. [Quoting from King and Wallace's book on page 16]:
“We should not confuse information stages with time periods. Stages model the flow of information; time periods represent the ticking of the clock in a model. Stages, on the other hand, are points in time where we make decisions in the model after having learned something new.”

 A: The staging does not explicitly state anything about the statistical relation of the variables, but rather tells us which conditional distributions we care about.
For example, suppose some variable A is a first stage variable and B is a second stage variable. Then, the two probability distributions we care about are $P(A)$ and $P(B | A)$. This is because at the first stage, we care about the value of $A$, which is unknown. Since $B$ is also unknown, what we care about is the marginal distribution of $A$. At the second stage, we know $A$ and care about $B$, thus we are working with $P(B|A)$. In contrast, the distribution $P(A|B)$ is irrelevant for our stochastic program. 
Note that this doesn't tell us anything about these quantities. For example, nothing restrains us from having $A$ and $B$ independent, although if we know they are, our problem just got easier.
Why is this important? Well, in traditional probability courses, we always think about computing the conditional distribution from a joint distribution. In statistics, we often ignore the joint distribution and directly model a conditional distribution. As an example, in logistic regression we often model $P(Y|X)$. However, we generally skip the step of modeling $P(X)$ and thus $P(Y,X)$. So in our staging example, we know that we need to model $P(A)$ and $P(B|A)$, but we can skip modeling $P(B)$ and $P(A,B)$. Note that in general, modeling joint distributions is considerably harder than conditional distributions!
