### Reciprocal links in structural equations

**From Dennis Lindley **

Equations (1.42) and (1.43) and the general issue of description by equations, still perplex me. It is incoherent to state both *p*(*x*|*y*) and *p*(*y*|*x*). (Try it with *x* and *y* binary, when these statements describe 4 values, whereas we know only 3 are needed for the joint distribution of *x* and *y*.) There are special cases, as with normal, linear regression, where the coherence is avoided. Generally I do not see how there can be two links between *x* and *y*.

The coherence problem you describe is precisely why we do not find any cycles in the graphical models used in statistics. We do find them in econometrics though. Graphical models in statistics are defined by conditional probability claims, while structural equations in general say nothing about

p(x|y) orp(y|x). (See footnote 4, page 137). The only claims these equations make are aboutp(x|do(y)) andp(y|do(x)) Moreover, unlikep(x|y) andp(y|x), there are no coherence constraints onp(x|do(y)) andp(y|do(x)). The only coherence constraints we need are:[tex]p(x|do(y)) ge p(x,y)quad {rm and}quad p(y|do(x)) ge p(x,y)[/tex]

(see Eq. (9.33), page 294) and these are satisfied automatically for all parameters in Equations (1.42) and (1.43), as long as the system has a unique solution.

Comment by judea — September 15, 2000 @ 12:00 am

A phone with a 5.7-inch display would be a bit larger than the iPhone 6 Plus, which has a 5.5-inch screen, but the same size as the Samsung Galaxy Note 4.The smaller phone will be manufactured by LG and the larger one will be made by Huawei, the report says.

Comment by Dior iPhone 6 Case — May 28, 2015 @ 12:35 am

Blog GizmoChina reported in March that Google may be partnering with Huawei for its upcoming Nexus phone, but it wasn’t until this month that we heard reports of Google also launching a second Nexus device. Before publishing to Android Police, Artem Russakovskii, who founded the website, mentioned the rumor on his personal Google+ page.

Comment by MCM iPhone 6 Case — May 28, 2015 @ 12:36 am