7,554 research outputs found
The Inflation Technique for Causal Inference with Latent Variables
The problem of causal inference is to determine if a given probability
distribution on observed variables is compatible with some causal structure.
The difficult case is when the causal structure includes latent variables. We
here introduce the for tackling this problem. An
inflation of a causal structure is a new causal structure that can contain
multiple copies of each of the original variables, but where the ancestry of
each copy mirrors that of the original. To every distribution of the observed
variables that is compatible with the original causal structure, we assign a
family of marginal distributions on certain subsets of the copies that are
compatible with the inflated causal structure. It follows that compatibility
constraints for the inflation can be translated into compatibility constraints
for the original causal structure. Even if the constraints at the level of
inflation are weak, such as observable statistical independences implied by
disjoint causal ancestry, the translated constraints can be strong. We apply
this method to derive new inequalities whose violation by a distribution
witnesses that distribution's incompatibility with the causal structure (of
which Bell inequalities and Pearl's instrumental inequality are prominent
examples). We describe an algorithm for deriving all such inequalities for the
original causal structure that follow from ancestral independences in the
inflation. For three observed binary variables with pairwise common causes, it
yields inequalities that are stronger in at least some aspects than those
obtainable by existing methods. We also describe an algorithm that derives a
weaker set of inequalities but is more efficient. Finally, we discuss which
inflations are such that the inequalities one obtains from them remain valid
even for quantum (and post-quantum) generalizations of the notion of a causal
model.Comment: Minor final corrections, updated to match the published version as
closely as possibl
An Orbital Stability Study of the Proposed Companions of SW Lyncis
We have investigated the dynamical stability of the proposed companions
orbiting the Algol type short-period eclipsing binary SW Lyncis (Kim et al.
2010). The two candidate companions are of stellar to sub-stellar nature, and
were inferred from timing measurements of the system's primary and secondary
eclipses. We applied well-tested numerical techniques to accurately integrate
the orbits of the two companions and to test for chaotic dynamical behaviour.
We carried out the stability analysis within a systematic parameter survey
varying both the geometries and orientation of the orbits of the companions, as
well as their masses. In all our numerical integrations we found that the
proposed SW Lyn multi-body system is highly unstable on time-scales on the
order of 1000 years. Our results cast doubt on the interpretation that the
timing variations are caused by two companions. This work demonstrates that a
straightforward dynamical analysis can help to test whether a best-fit
companion-based model is a physically viable explanation for measured eclipse
timing variations. We conclude that dynamical considerations reveal that the
propsed SW Lyncis multi-body system most likely does not exist or the
companions have significantly different orbital properties as conjectured in
Kim et al. (2010).Comment: 9 pages, 6 figures, 2 tables. Submitted to and accepted by JASS --
Journal for Astronomy and Space Sciences (using JKAS LaTeX style file
A Report on Our Eight Years With the Church in Europe
https://digitalcommons.acu.edu/crs_books/1283/thumbnail.jp
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