[FRIAM] PM-2017-MethodologicalBehaviorismCausalChainsandCausalForks(1).pdf

[jon zingale]

"""
The notion of Screening Off comes from the act of “marking” a subset of
the coins, to get at the sense in which their states may stand between
the future states of some other focal coins you may wish to discuss, and
the universe of other coins whose states you want to know if you can
ignore.  But the “screening” part of Screening Off comes from the
peer-status of any coin to any other coin, in context of a network that
is provided to you as context.
"""

I find this elaboration helpful. The metaphor of Screening Off seems
right to me in that it is not a walling off, but rather acting *as if*
something was in a different room though it is not, “marking”. Once we
introduce marked variables, the bookkeeping has a calculus all its own.
>From a SEP article[S], there is a nice explication of Screening Off from
the perspective of a Markov condition:

  For every variable X in V, and every set of variables Y ⊆ V ∖ DE(X),
  P(X ∣ PA(X) & Y) = P(X ∣ PA(X)).

  where DE(X) is the collection of descendants of X, PA(X) the parents.

This definition highlights the arbitrary nature of Screening Off.
Y may be a parent of X, in which case, the triviality comes from claiming
that we can cancel the redundant Y as it already is accounted for. In
the other case, we can cancel Y because it has no causal effect on X.

>From the Sober paper, I gather that the introduction of an intermediate
stage (X) into his 'V' model gives rise to a 'Y' model which screens off
some initial stage (S) from later stages (R1, R2)[?]. He further asserts
(and this would better be addressed by a practicing bayesian) that this
introduction is non-trivial. Riffing off of Glen's comments, allow me
a bit more rope to hang myself. X depends causally on S, the total
effect of S on the later network is present at X and therefore the result
of X and the probability associated with X is sufficient for causation
at R1 and R2. However, wrt the stage of definition S, X introduces some
uncertainty having the effect of correlating uncertainty in A and B, a
possibly uncertain representation is an uncertain representation.

In the 'V' model we have a lack of dependence and a Screening Off. This
then is also the case for R1 and R2 conditioned on X in the 'Y' model.
However, with respect to conditioning on S in the 'Y' model, uncertainty
creeps in. Now, like quantum states, R1 & R2 relative to S, cannot be
written in product form and so they must be handled as an irreducible,
entangled.

I am not sure that this post contributes much to what others have
already said, but I wanted to struggle on a bit.

[S] https://plato.stanford.edu/entries/causation-probabilistic/

[?] A continued point of confusion for me, relative to the paper, is
determining whether the Screening Off is between R1 and R2 or between S
and (R1, R2) or both. The other confusion for me occurs because Screening
Off is a cancellation property on the condition and he appears to want
to apply screening to variables *left of the bar*. I likely just need to sit
with it a bit, but any clarifications are welcome. 



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