""" 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/
