more robust U-turn checking #145
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See <https://discourse.mc-stan.org/t/nuts-misses-u-turns-runs-in-circles-until-max-treedepth/9727/>. Incidental changes: minor doc fixes, more NUTS tests where they belong.
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Summary: Pull Request resolved: #864 An issue with the U-turn condition was discovered and discussed in [this post in Stan forum](https://discourse.mc-stan.org/t/nuts-misses-u-turns-runs-in-circles-until-max-treedepth/9727) TL;DR: we can make the U-turn condition more robust by introducing two additional checks across subtrees. This can help us avoid missing U-turns for approximately iid normal models. {F619223264} Since the tree combining code are almost identical in `_build_tree` and `propose`, I also take the chance to refactor them into a common function called `_combine_tree`. If you look closely you will notice that most part of `_combine_tree` are moved from existing code as-is. The only addition is the two additional call to `_is_u_turning` Related PR that implements this change: - Stan: stan-dev/stan#2800 - PyMC3: pymc-devs/pymc#3605 - Turing.jl: TuringLang/AdvancedHMC.jl#207 - DynamicHMC.jl: tpapp/DynamicHMC.jl#145 Reviewed By: neerajprad Differential Revision: D28735950 fbshipit-source-id: ada4ebcad26a87ef5e697f422b5c5b17007afe42
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Fixes #115. See discussion at Stan forum.