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

[Frank Wimberly]

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

I believe my example using (A -> B -> C) is a very specific example of this.

Frank

On Thu, Feb 11, 2021 at 9:43 AM jon zingale <jonzingale at gmail.com> wrote:

> """
> 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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-- 
Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918

Research:  https://www.researchgate.net/profile/Frank_Wimberly2
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