To cite the posterior R package:

Bürkner P, Gabry J, Kay M, Vehtari A (2025). “posterior: Tools for Working with Posterior Distributions.” R package version 1.6.1, https://mc-stan.org/posterior/.

To cite the MCMC convergence diagnostics (`rhat`, `ess_bulk`, `ess_tail`, `ess_median`, `ess_quantile`, `mcse_median`, and `mcse_quantile`):

Vehtari A, Gelman A, Simpson D, Carpenter B, Bürkner P (2021). “Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC (with discussion).” Bayesian Analysis, 16(2), 667-718.

To cite MCMC convergence diagnostic `nested_rhat`:

Margossian C, Hoffman M, Sountsov P, Riou-Durand L, Vehtari A, Gelman A (2024). “Nested Rhat: Assessing the convergence of Markov chain Monte Carlo when running many short chains.” Bayesian Analysis. doi:10.1214/24-BA1453.

To cite MCMC convergence diagnostic `rstar`:

Lambert B, Vehtari A (2022). “Rstar: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.” Bayesian Analysis, 17(2), 353-379. doi:10.1214/20-BA1252.

To cite Pareto-k diagnostics and Pareto smoothing (`pareto_khat`, `pareto_min_ss`, `pareto_convergence_rate`, `khat_threshold`, `pareto_diags`, and `pareto_smooth`):

Vehtari A, Simpson D, Gelman A, Yao Y, Gabry J (2024). “Pareto smoothed importance sampling.” Journal of Machine Learning Research, 25(72), 1-58.

Corresponding BibTeX entries:

  @Misc{,
    title = {posterior: Tools for Working with Posterior
      Distributions},
    author = {Paul-Christian Bürkner and Jonah Gabry and Matthew Kay
      and Aki Vehtari},
    year = {2025},
    note = {R package version 1.6.1},
    url = {https://mc-stan.org/posterior/},
  }

  @Article{,
    title = {Rank-normalization, folding, and localization: An improved
      Rhat for assessing convergence of MCMC (with discussion)},
    author = {Aki Vehtari and Andrew Gelman and Daniel Simpson and Bob
      Carpenter and Paul-Christian Bürkner},
    journal = {Bayesian Analysis},
    year = {2021},
    volume = {16},
    number = {2},
    pages = {667-718},
  }

  @Article{,
    title = {Nested Rhat: Assessing the convergence of Markov chain
      Monte Carlo when running many short chains},
    author = {Charles C. Margossian and Matthew D. Hoffman and Pavel
      Sountsov and Lionel Riou-Durand and Aki Vehtari and Andrew
      Gelman},
    journal = {Bayesian Analysis},
    year = {2024},
    doi = {10.1214/24-BA1453},
  }

  @Article{,
    title = {Rstar: A robust MCMC convergence diagnostic with
      uncertainty using decision tree classifiers},
    author = {Ben Lambert and Aki Vehtari},
    journal = {Bayesian Analysis},
    year = {2022},
    volume = {17},
    number = {2},
    pages = {353-379},
    doi = {10.1214/20-BA1252},
  }

  @Article{,
    title = {Pareto smoothed importance sampling},
    author = {Aki Vehtari and Daniel Simpson and Andrew Gelman and
      Yuling Yao and Jonah Gabry},
    journal = {Journal of Machine Learning Research},
    year = {2024},
    volume = {25},
    number = {72},
    pages = {1-58},
  }