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I just started a doctoral program in psychology, and my research interest concerns causal reasoning. Since Pearl's Causality, the popularity of causal Bayes nets as psychological models for causal reasoning has really grown. Initially, I had some serious reservations, but now I'm beginning to think a great many of these are due in part to the oversimplified treatment that CBNs get in the psychology literature. For instance, the distinction between a) directed acyclic graphs + underlying conditional probabilities, and b) functional causal models, is rarely mentioned. Ignoring this distinction leads to some weird results, especially when the causal system in question has prominent physical mechanisms.
Say we represent Gear A as causing Gear B to turn because Gear A is hooked up to an engine, and because the two gears are connected to each other by a chain. Something like this:
Engine(ON) -> GearA(turn) -> GearB(turn)
As a causal Net, this is problematic. If I "intervene" on GearA (perform do(GearA=stop)), then I get the expected result: GearA stops, GearB stops, and the engine keeps running (the 'undoing' effect [Sloman, 2005]). But what happens if I "intervene" on GearB? Since they are connected by a chain, GearA would stop as well. But GearA is the cause, and GearB is the effect: intervening on effects is NOT supposed to change the status of the cause. This violates a host of underlying assumptions for causal Bayes nets. (And you can't represent the gears as causing each other's movement, since that'd be a cyclical graph.)
However, this can be solved if we're not representing the system as the above net, but we're instead representing the physics of the system, representing the forces involved via something that looks vaguely like newtonian equations. Indeed, this would accord better with people's hypothesis-testing behavior: if they aren't sure which gear has the engine behind it, they wouldn't try "intervening" on GearA's motion and GearB's motion, they'd try removing the chain, and seeing which gear is still moving.
At first it seemed to me like causal Bayes nets only do the first kind of representation, not the latter. However, I was wrong: Pearl's "functional causal models" appear to do the latter. These have been vastly less prevalent in the psych literature, yet they seem extremely important.
Anyways, the moral of the story is that I should really read a lot of Pearl's Causality, and actually have a grasp of some of the math; I can't just read the first chapter like most psychology researchers interested in this stuff.
I'm not much of an autodidact when it comes to math, though I'm good at it when put in a class. Can anyone who's familiar with Pearl's book give me an idea of what sort of prerequisites it would be good to have in order to understand important chunks of it? Or am I overthinking this, and I should just try and plow through.
Any suggestions on classes (or textbooks, I guess), or any thoughts on the above gears example, will be helpful and welcome.
EDIT: Maybe a more specific request could be phrased as following: will I be better served by taking some extra computer science classes, or some extra math classes (i.e., on calculus and probabilistic systems)?