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References

This is a list of references for the methods implemented in ArviZ (including base/stats/plots). The references are organized by diagnosis. The format is the one used for docstrings. We could have references in BibTeX format, and use https://sphinxcontrib-bibtex.readthedocs.io/en/latest/ to include them in the docstring of each function and in a single webpage. See https://github.com/arviz-devs/arviz-stats/issues/56

Psense

References
----------
.. [1] Kallioinen et al. *Detecting and diagnosing prior and likelihood sensitivity with
    power-scaling*, Stat Comput 34(57) (2024), https://doi.org/10.1007/s11222-023-10366-5

LOO

References
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.. [1] Vehtari et al. *Practical Bayesian model evaluation using leave-one-out cross-validation
    and WAIC*. Statistics and Computing. 27(5) (2017). https://doi.org/10.1007/s11222-016-9696-4.
    arXiv preprint https://arxiv.org/abs/1507.04544.

.. [2] Yao et al. *Using stacking to average Bayesian predictive distributions*
    Bayesian Analysis, 13, 3 (2018). https://doi.org/10.1214/17-BA1091 
    arXiv preprint https://arxiv.org/abs/1704.02030.

.. [3] Vehtari et al. *Pareto Smoothed Importance Sampling*.
    Journal of Machine Learning Research, 25(72) (2024). https://jmlr.org/papers/v25/19-556.html.
    arXiv preprint https://arxiv.org/abs/1507.02646

.. [4] Magnusson et al. *Bayesian Leave-One-Out Cross-Validation for Large Data.*
    Proceedings of the 36th International Conference on Machine Learning, 97 (2019)
    https://proceedings.mlr.press/v97/magnusson19a.html
    arXiv preprint https://arxiv.org/abs/1904.10679

R-hat, ESS, MCSE

References
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.. [1] Vehtari et al. *Rank-normalization, folding, and localization: An improved Rhat for
    assessing convergence of MCMC*. Bayesian Analysis. 16(2) (2021)
    https://doi.org/10.1214/20-BA1221. arXiv preprint https://arxiv.org/abs/1903.08008

PAV-adjusted calibration plot

References
----------
.. [1] Dimitriadis et al. *Stable reliability diagrams for probabilistic classifiers*.
    PNAS, 118(8) (2021). https://doi.org/10.1073/pnas.2016191118

.. [2] Säilynoja et al. *Recommendations for visual predictive checks in Bayesian workflow*. 
    (2025) arXiv preprint https://arxiv.org/abs/2503.01509

Energy plot and divergences

References
----------
.. [1] Betancourt. *Diagnosing Suboptimal Cotangent Disintegrations in
    Hamiltonian Monte Carlo*. (2016) https://arxiv.org/abs/1604.00695

Rootograms

References
----------
.. [1] Kleiber et al. *Visualizing Count Data Regressions Using Rootograms*. 
    The American Statistician, 70(3). (2016) https://doi.org/10.1080/00031305.2016.1173590

.. [2] Säilynoja et al. *Recommendations for visual predictive checks in Bayesian workflow*. 
    (2025) arXiv preprint https://arxiv.org/abs/2503.01509

ECDF-pit

References
----------
.. [1] Säilynoja et al. *Graphical test for discrete uniformity and
   its applications in goodness-of-fit evaluation and multiple sample comparison*.
   Statistics and Computing 32(32). (2022) https://doi.org/10.1007/s11222-022-10090-6

Bayesian R2

References
----------
.. [1] Gelman et al. *R-squared for Bayesian regression models*.
   The American Statistician, 73(3). (2019) https://doi:10.1080/00031305.2018.1549100
   preprint http://www.stat.columbia.edu/~gelman/research/unpublished/bayes_R2_v3.pdf