To cite the loo R package:

Vehtari A, Gabry J, Magnusson M, Yao Y, Bürkner P, Paananen T, Gelman A (2025). “loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models.” R package version 2.9.0, https://mc-stan.org/loo/.

To cite the loo paper:

Vehtari A, Gelman A, Gabry J (2017). “Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC.” Statistics and Computing, 27, 1413–1432. doi:10.1007/s11222-016-9696-4.

To cite when using loo_compare():

Sivula T, Magnusson M, Matamoros A, Vehtari A (2025). “Uncertainty in Bayesian leave-one-out cross-validation based model comparison.” Bayesian Analysis. doi:10.1214/24-BA1453.

To cite the stacking paper:

Yao Y, Vehtari A, Simpson D, Gelman A (2018). “Using stacking to average Bayesian predictive distributions.” Bayesian Analysis, 13, 917–1007. doi:10.1214/17-BA1091.

To cite Pareto-k diagnostics:

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

To cite moment matching:

Paananen T, Piironen J, Buerkner P, Vehtari A (2021). “Implicitly adaptive importance sampling.” Statistics and Computing, 31, 16.

To cite subsampling loo:

Magnusson M, Andersen M, Jonasson J, Vehtari A (2019). “Leave-One-Out Cross-Validation for Large Data.” In Thirty-sixth International Conference on Machine Learning, volume 97, 4244-4253.

To cite subsampling loo:

Magnusson M, Andersen M, Jonasson J, Vehtari A (2019). “Leave-One-Out Cross-Validation for Model Comparison in Large Data.” In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), volume 108, 341-351.

Corresponding BibTeX entries:

  @Misc{,
    title = {loo: Efficient leave-one-out cross-validation and WAIC for
      Bayesian models},
    author = {Aki Vehtari and Jonah Gabry and Måns Magnusson and Yuling
      Yao and Paul-Christian Bürkner and Topi Paananen and Andrew
      Gelman},
    year = {2025},
    note = {R package version 2.9.0},
    url = {https://mc-stan.org/loo/},
  }

  @Article{,
    title = {Practical Bayesian model evaluation using leave-one-out
      cross-validation and WAIC},
    author = {Aki Vehtari and Andrew Gelman and Jonah Gabry},
    year = {2017},
    journal = {Statistics and Computing},
    volume = {27},
    issue = {5},
    pages = {1413--1432},
    doi = {10.1007/s11222-016-9696-4},
  }

  @Article{,
    title = {Uncertainty in Bayesian leave-one-out cross-validation
      based model comparison},
    author = {Tuomas Sivula and Måns Magnusson and Asael Alonzo
      Matamoros and Aki Vehtari},
    journal = {Bayesian Analysis},
    year = {2025},
    note = {doi:10.1214/24-BA1453},
  }

  @Article{,
    title = {Using stacking to average Bayesian predictive
      distributions},
    author = {Yuling Yao and Aki Vehtari and Daniel Simpson and Andrew
      Gelman},
    journal = {Bayesian Analysis},
    year = {2018},
    volume = {13},
    issue = {3},
    pages = {917--1007},
    doi = {10.1214/17-BA1091},
  }

  @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},
  }

  @Article{,
    author = {Topi Paananen and Juho Piironen and Paul-Christian
      Buerkner and Aki Vehtari},
    title = {Implicitly adaptive importance sampling},
    journal = {Statistics and Computing},
    volume = {31},
    pages = {16},
    year = {2021},
  }

  @InProceedings{,
    author = {Måns Magnusson and Michael Riis Andersen and Johan
      Jonasson and Aki Vehtari},
    title = {Leave-One-Out Cross-Validation for Large Data},
    booktitle = {Thirty-sixth International Conference on Machine
      Learning},
    publisher = {PMLR},
    volume = {97},
    pages = {4244-4253},
    year = {2019},
  }

  @InProceedings{,
    author = {Måns Magnusson and Michael Riis Andersen and Johan
      Jonasson and Aki Vehtari},
    title = {Leave-One-Out Cross-Validation for Model Comparison in
      Large Data},
    booktitle = {Proceedings of the 23rd International Conference on
      Artificial Intelligence and Statistics (AISTATS)},
    publisher = {PMLR},
    volume = {108},
    pages = {341-351},
    year = {2019},
  }