the word on the street

Books with Examples Translated to Stan

Eric-Jan Wagenmakers and Michael D. Lee. 2014. Bayesian Cognitive Modeling: A Practical Course. Cambridge Univesity Press.
Lunn, D., Jackson, C., Best, N., Thomas, A., and Spiegelhalter, D. 2013. The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman & Hall/CRC Press.
Marc Kéry and Michael Schaub. 2011. Bayesian Population Analysis using WinBUGS: A hierarchical perspective. Academic Press. [chapters 3–10]
Andrew Gelman and Jennifer Hill. 2009. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. [second edition being updated to 100% Stan implementations]

Code may be found in the Stan example models repo.

Papers about Stan

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). 10.18637/jss.v076.i01
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.
Robert L. Grant, Daniel C. Furr, Bob Carpenter, and Andrew Gelman. 2016. Fitting Bayesian item response models in Stata and Stan. arXiv 1601.03443.
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, NIPS.
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.

Michael Betancourt. 2017. A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434.
Cole C. Monnahan, James T. Thorson, and Trevor A. Branch. 2016. Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo. Methods in Ecology and Evolution.
Michael J. Betancourt. 2016. Identifying the Optimal Integration Time in Hamiltonian Monte Carlo. arXiv:1601.00225.
Matthew D. Hoffman and Andrew Gelman. 2014. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. 15(Apr):1593–1623.
Michael J. Betancourt, Mark Girolami. 2013. Hamiltonian Monte Carlo for Hierarchical Models. arXiv 1312.0906.
Michael J. Betancourt. 2013. A General Metric for Riemannian Manifold Hamiltonian Monte Carlo. arXiv 1212.4693.
Michael J. Betancourt. 2013. Generalizing the No-U-Turn Sampler to Riemannian Manifolds. arXiv 1304.1920.
Radford Neal. 2011. http://www.mcmchandbook.net/HandbookChapter5.pdf. In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng. Chapman-Hall/CRC.

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.
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.

McElreath, R. rethinking: Statistical Rethinking book package, version 1.58. GitHub project rmcelreath/rethinking. Language: R
Bürkner, P.-C. brms: Bayesian Regression Models using Stan. CRAN package brms. Language: R
Facebook. PROPHET: Forecasting at Scale. Languages: R and Python

Additional CRAN packages using Stan in R can be found in the reverse links from the packages rstan and rstanarm.

ICON, plc. 2017. NONMEM 7.4, Nonlinear mixed effects models for pharmacometrics. [commercial paid license, not open source]
PyMC Developers. 2016. PyMC3: Probabilistic programming in Python. GitHub project pymc-devs/pymc3.