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Explain Query Bounds - #212

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Explain Query Bounds#212
willGraham01 wants to merge 12 commits into
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wgraham/208-query-bounds-docs

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@willGraham01 willGraham01 commented Aug 7, 2026

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Resolves #208 (hopefully!)

An attempt by me to explain the problem we're trying to solve, in particular in reference to the somewhat bare final section of the continuous treatments document.

This means a re-write of the old simple example and introductory theory section, to better fit the framework that we're now using. The actual definitions are rather involved, but it's either that or no definitions at all, so went mostly all-in on the maths. Did try to provide an intuitive picture in the README introduction though.

The new theory/index.md hopefully clears up what we mean by causal model, causal problem, and causal response function. The long-and-short of it is that the "query bounds on the causal response" are essentially the extrema of some quantity that our class of causal models can predict, but the admissible models are forced to the "$\epsilon$-close" to reality.

Note that removing the glossary also throws away some of the terminology we were trying to establish surrounding "parameter", but with our new approach this ambiguity around the term "parameter" is gone, since the nodes now use the inputs, parameters structure for their compute attributes (and the older DistributionNode types that used the parameter terminology are redundant, for now).

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Clear up ambiguity in the Query bounds on causal response section of docs/theory/continuous-treatements.md

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