Causal Analysis in Theory and Practice

June 28, 2000

On causality and decision trees

Filed under: Decision Trees,General — moderator @ 12:00 am

From Dennis Lindley:

If your assumption, that controlling X at x is equivalent to removing the function for X and putting X=x elsewhere, is applicable, then it makes sense because, from my last paragraph, we need past information to select the correct function. What I do not understand at the moment is the relevance of this to decision trees. At a decision node, one conditions on the quantities known at the time of the decision. At a random node, one includes all relevant uncertain quantities under known conditions. Nothing more than the joint distributions (and utility considerations) are needed. For example, in the medical case, the confounding factor may either be known or not at the time the decision about treatment is made, and this determines the structure of the tree. Where causation may enter is when the data are used to assess the probabilities needed in the tree, and it is here that Novick and I used exchangeability. The Bayesian paradigm makes a sharp distinction between probability as belief and probability as frequency, calling the latter, chance. If I understand causation, it would be reasonable that our concept could conveniently be replaced by yours in this context.

June 10, 2000

On functional models for predicting the effect of actions

Filed under: Book (J Pearl),General — moderator @ 12:00 am

From Dennis Lindley:

In the part of Chapter 1 that you kindly sent me, a functional, causal model is clearly defined by a set of equations in (1.40). The set provides a joint probability distribution of the variables using a specific order. That distribution may be manipulated to obtain an equivalent probability specification in any other order. I showed in my note that this probability structure could be described by a set of equations in an order different from that of (1.40). (That proof may be wrong, though on p. 31 you suggest the result was known in '93.) Consequently (1.40) can be replaced by a different set of equations. You tell us now to see what happens were a variable to be controlled; this in terms of the set, and I showed that different consequences flowed if different sets were used. How do I decide which set is correct?

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