References
Ayer, Miriam, H. D. Brunk, G. M. Ewing, W. T. Reid, and Edward
Silverman. 1955. “An Empirical Distribution
Function for Sampling with Incomplete Information.”
The Annals of Mathematical Statistics 26 (4): 641–47. https://doi.org/10.1214/aoms/1177728423.
Brockmann, H. Jane. 1996. “Satellite Male Groups in Horseshoe
Crabs, Limulus Polyphemus.” Ethology 102 (1): 1–21. https://doi.org/10.1111/j.1439-0310.1996.tb01099.x.
Dimitriadis, Timo, Tilmann Gneiting, and Alexander I. Jordan. 2021.
“Stable Reliability Diagrams for Probabilistic
Classifiers.” Proceedings of the National Academy of
Sciences 118 (8): e2016191118. https://doi.org/10.1073/pnas.2016191118.
Gabry, Jonah, Daniel Simpson, Aki Vehtari, Michael Betancourt, and
Andrew Gelman. 2019. “Visualization in Bayesian Workflow.”
Journal of the Royal Statistical Society Series A: Statistics in
Society 182 (2): 389–402. https://doi.org/10.1111/rssa.12378.
Gelman, Andrew. 2008. The Folk Theorem of Statistical
Computing. https://statmodeling.stat.columbia.edu/2008/05/13/the_folk_theore/.
Gelman, Andrew. 2013. “Two simple examples
for understanding posterior p-values whose distributions are far from
uniform.” Electronic Journal of Statistics 7
(none): 2595–602. https://doi.org/10.1214/13-EJS854.
Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki
Vehtari, and Donald B. Rubin. 2013. Bayesian Data
Analysis. Boca Raton. https://doi.org/10.1201/b16018.
Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from
Iterative Simulation Using Multiple Sequences.”
Statistical Science 7 (4). https://doi.org/10.1214/ss/1177011136.
Hoyer, Stephan, and Joe Hamman. 2017. “Xarray:
N-D Labeled Arrays
and Datasets in Python.” Journal of
Open Research Software 5 (1). https://doi.org/10.5334/jors.148.
Johnson, Roger W. 1996. “Fitting Percentage of
Body Fat to Simple Body Measurements.”
Journal of Statistics Education 4 (1): 6. https://doi.org/10.1080/10691898.1996.11910505.
Kallioinen, Noa, Topi Paananen, Paul-Christian Bürkner, and Aki Vehtari.
2024. “Detecting and Diagnosing Prior and Likelihood Sensitivity
with Power-Scaling.” Statistics and Computing 34 (1):
57. https://doi.org/10.1007/s11222-023-10366-5.
Kleiber, Christian, and Achim Zeileis. 2016. “Visualizing Count
Data Regressions Using Rootograms.” The American
Statistician 70 (3): 296–303. https://doi.org/10.1080/00031305.2016.1173590.
Margossian, Charles C., Matthew D. Hoffman, Pavel Sountsov, Lionel
Riou-Durand, Aki Vehtari, and Andrew Gelman. 2025. “Nested
R^: Assessing the Convergence of
Markov Chain Monte Carlo When Running Many Short
Chains.” Bayesian Analysis 20 (4): 1587–614. https://doi.org/10.1214/24-BA1453.
Meng, Xiao-Li. 1994. “Posterior Predictive p-Values.” The
Annals of Statistics 22 (3): 1142–60. https://doi.org/10.1214/aos/1176325622.
Nguyen, Hoang-Vu, and Jilles Vreeken. 2015. “Non-Parametric
Jensen-Shannon Divergence.” In Machine
Learning and Knowledge Discovery in
Databases, edited by Annalisa Appice, Pedro Pereira
Rodrigues, Vítor Santos Costa, João Gama, Alípio Jorge, and Carlos
Soares, vol. 9285. Springer International Publishing. https://doi.org/10.1007/978-3-319-23525-7_11.
Säilynoja, Teemu, Andrew R. Johnson, Osvaldo A. Martin, and Aki Vehtari.
2025. Recommendations for Visual Predictive Checks in Bayesian
Workflow. https://arxiv.org/abs/2503.01509.
Soch, Joram, Thomas J Faulkenberry, Kenneth Petrykowski, and Carsten
Allefeld. 2024. The Book of Statistical Proofs. https://doi.org/10.5281/ZENODO.4305949.
Suorsa, Saku, and Aki Vehtari. 2026. Predictive Assessment and
Comparison of Bayesian Survival Models for Cancer Recurrence. https://arxiv.org/abs/2601.01662.
Tesso, Herman, and Aki Vehtari. 2026. LOO-PIT Predictive Model
Checking. https://arxiv.org/abs/2603.02928.
Tukey, John W. 1977. Exploratory Data
Analysis. 1 edition. Pearson. https://archive.org/details/exploratorydataa0000tuke_7616/mode/2up.
Vehtari, Aki, Andrew Gelman, Daniel Simpson, Bob Carpenter, and
Paul-Christian Bürkner. 2021. “Rank-Normalization,
Folding, and Localization: An Improved
R^ for Assessing Convergence of MCMC
(with Discussion).” Bayesian Analysis 16
(2): 667–718. https://doi.org/10.1214/20-BA1221.
Vehtari, Aki, Daniel Simpson, Andrew Gelman, Yuling Yao, and Jonah
Gabry. 2024. “Pareto Smoothed Importance Sampling.”
Journal of Machine Learning Research 25 (72): 1–58.
Venables, W. N., and Brian D. Ripley. 2002. Modern Applied
Statistics with s. 4th ed. Springer.