
The Three Layer Causal Hierarchy [pdf] - dstein64
http://web.cs.ucla.edu/~kaoru/3-layer-causal-hierarchy.pdf
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kgwgk
Context:
[http://andrewgelman.com/2016/07/07/30608/#comment-283490](http://andrewgelman.com/2016/07/07/30608/#comment-283490)

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Bromskloss
I still don't know how to convince myself that causal relationships exist at
all and that everything isn't just things like correlations, that would go
into level 1 in this hierarchy if Pearl's.

~~~
ced
I'll try...

Rain causes people to be wet. This implies that if we were to God-like stop
the rain, people wouldn't be wet. But if we were to prevent people from being
wet (by buying them an umbrella), that wouldn't stop the rain. This is not
something you can infer from correlations alone.

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Retra
That's far too little logic to be a counterexample here. Rain correlates with
a lot of things. If you were to stop _all of those things_ , you could surely
stop the rain as well. For instance, if rain is correlated with clouds, and
you get rid of clouds, you'll get rid of rain. The fact is, there does not
exist this thing you've called 'rain' that causes people to be wet and does
nothing else relevant to your argument.

There's plenty of reason to believe that causal relationships are structural
simplifications of correlative ones. We just don't have any great
formalizations of them.

~~~
mistersheik
> If you were to stop all of those things, you could surely stop the rain as
> well.

By the way, this is not true in general. Suppose B…F are sampled from Boolean
variables with bias 0.5. A Boolean circuit like A = (sum(B,C,D,E,F)>3) + (not
B and not C and… not F). A is correlated with all of its causes B through F.
However, stopping all of its causes, causes A to turn on.

> If you were to stop all of those things, you could surely stop the rain as
> well.

But, you typically can't intervene everywhere. For example, you may not have
any power over the gardener who normally turns the sprinkler on. The point of
interventions (like turning a sprinkler on) is that you can reason about what
would happen.

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Retra
"B...F" are not all the causes of A. You forgot to include the relation
"f(B...F)", whose existence is also strongly correlated with A, as per the
entire justification for using that '=' symbol the way you have.

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mistersheik
This is really well-written, so I looked up the author, and no surprise it's
Judea Pearl.

