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 <[email protected]> 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. > > > > -- > Sent from: http://friam.471366.n2.nabble.com/ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ > -- 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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