Published Articles and Books

Stan Language and Algorithms

• Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. Stan: A probabilistic programming language. Journal of Statistical Software 76(1).

• Andrew Gelman, Daniel Lee, and Jiqiang Guo. 2015. Stan: A probabilistic programming language for Bayesian inference and optimization. Journal of Education and Behavioral Statistics. 40(5):530–543.

• Alp Kucukelbir, Rajesh Ranganath, Andrew Gelman and David M. Blei. 2015. Automatic variational inference in Stan

• Lu Zhang, Bob Carpenter, Andrew Gelman, Aki Vehtari. 2022. Pathfinder: Parallel quasi-Newton variational inference Journal of Machine Learning Research. 23(306):1−49, 2022.

• Michael Betancourt. 2017. A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434.

• Matthew D. Hoffman, Andrew Gelman. 2014. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. 15(47):1593−1623.

• Cole C. Monnahan, James T. Thorson, and Trevor A. Branch. 2017. Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo Methods in Ecology and Evolution. 8(3):339-348.

• Radford Neal. 2011. MCMC Using Hamiltonian Dynamics. In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng. Chapman-Hall/CRC.

• Bob Carpenter, Matthew D. Hoffman, Marcus Brubaker, Daniel Lee, Peter Li, and Michael J. Betancourt. 2015. The Stan Math Library: Reverse-Mode Automatic Differentiation in C++.   arXiv 1509.07164.

Bayesian Workflow

• Andrew Gelman, Aki Vehtari, Daniel Simpson, Charles C. Margossian, Bob Carpenter, Yuling Yao, Lauren Kennedy, Jonah Gabry, Paul-Christian Bürkner, Martin Modrák. 2020. Bayesian Workflow

• Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, Paul-Christian Bürkner, 2021. Rank-Normalization, Folding, and Localization: An Improved R-hat for Assessing Convergence of MCMC (with Discussion) Bayesian Analysis 16(2).

• Aki Vehtari, Andrew Gelman, and Jonah Gabry. 2016. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. doi:10.1007/s11222-016-9696-4.

• Jonah Gabry, Daniel Simpson, Aki Vehtari, Michael Betancourt, Andrew Gelman. 2019 Visualization in Bayesian workflow. Journal of the Royal Statistical Society Series A: Statistics in Society 182(2):389–402.

• Robert L. Grant, Daniel C. Furr, Bob Carpenter, and Andrew Gelman. 2016. Fitting Bayesian item response models in Stata and Stan. arXiv 1601.03443.

Books using Stan

• Gelman, A., Hill, J., and Vehtari A. 2020. Regression and Other Stories

• Gelman, A. and Vehtari A. 2024. Active Statistics

• Korner-Nievergelt, F., Roth, T., Von Felten, S., Guélat, J., Almasi, B. and Korner-Nievergelt, P. 2024. Bayesian Data Analysis in Ecology Using Linear Models with R and Stan. Online.

• Suzuki, J. 2023. WAIC and WBIC with R Stan: 100 Exercises for Building Logic. Springer.

• Matsuura, K.. 2022. Bayesian Statistical Modeling with Stan, R, and Python. Springer.

• Johnson, A.A., M. Q. Ott, M. Dogucu. 2021. Bayes Rules! An Introduction to Applied Bayesian Modeling CRC Press.

• Holmes, E. E., M. D. Scheuerell, and E. J. Ward. 2019. Applied Time Series Analysis for Fisheries and Environmental Sciences. NOAA Fisheries, Northwest Fisheries Science Center.

• Hilbe, J. M., R.S. de Souza, and E. E. O. Ishida. 2017. Bayesian Models for Astrophysical Data Using R, JAGS, Python and Stan. Cambridge University Press.

• Matsuura, K.. 2016. Bayesian Statistical Modeling Using Stan and R. Wonderful R Series, Volume 2. Kyoritsu Shuppan Co., Ltd. [in Japanese]

• McElreath, R. 2016. Statistical Rethinking: A Bayesian Course with R and Stan. Chapman-Hall/CRC.

• Korner-Nievergelt, F., Roth, T., Von Felten, S., Guélat, J., Almasi, B. and Korner-Nievergelt, P. 2015. Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan. Academic Press.

• Kruschke, J. 2014. Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. Academic Press.

• Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. and Rubin, D.B. 2013. Bayesian Data Analysis, Third Edition. Chapman-Hall/CRC.