Add nested Rhat diagnostic - #907
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Implement nested R-hat (Margossian et al. 2024) following Definition 2.2 of the paper. This diagnostic generalises the classical potential scale reduction factor to a nested design where chains are grouped into superchains, making it well-suited for GPU-friendly samplers that run many short chains in parallel. Closes blackjax-devs#278 Co-authored-by: giladturok (PR blackjax-devs#752 — prior partial implementation)
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Closes #278.
Implements the nested$\hat{R}$ diagnostic from Margossian et al. (2024,
Bayesian Analysis), Definition 2.2 (equations 6-8). Useful for
hierarchical models where chains are grouped into superchains — catches
convergence failures that classical Rhat misses when between-superchain
variance is high.
When
M=1(single superchain), reduces to classical Rhat per Remark 2.3.Prior work: #752 implemented the core logic but was abandoned before tests
were added (Oct 2024). This is a fresh implementation with full test coverage.
Tests: 28 new test cases (172/172 diagnostics tests pass).