Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization

Journal of Educational and Behavioral Statistics

Volumn 40, Issue 5, 2015, Pages 530-543

  Gelman, Andrew ^a   Lee, Daniel ^a   Guo, Jiqiang ^b  

^a Columbia University ^*  (United States)

^b NPD Group   (United States)

Author keywords

Bayesian inference; hierarchical models; probabilistic programming; statistical computing

Indexed keywords

EID: 84945296911     PISSN: 10769986     EISSN: 19351054     Source Type: Journal    
DOI: 10.3102/1076998615606113     Document Type: Article

References (24)

1. D.BatesM.MaechlerB.BolkerS.Walker. (2014). lme4: Linear mixed-effects models using Eigen and S4[Computer software manual]. Retrieved fromhttp://CRAN.R-project.org/package=lme4(R package version 1.1-7)
2. S.BealL.SheinerA.BoeckmannR.Bauer. (1989–2009). NONMEM user’s guides[Computer software manual]. Ellicott City, MD: ICON Development Solutions.
3. M.Betancourt (2013). Generalizing the no-U-turn sampler to Riemannian manifolds. arXiv, 1304.1920. Retrieved fromhttp://arxiv.org/abs/1304.1920
4. R.H.ByrdP.LuJ.NocedalC.Zhu (1994). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, 1190–1208.
5. D.M.Gay. (2005). Semiautomatic differentiation for efficient gradient computations. In H.M.BückerG.F.CorlissP.HovlandU.NaumannB.Norris (Eds.), Automatic differentiation: Applications, theory, and implementations (Vol. 50, pp. 147–158). New York, NY: Springer. doi:10.1007/3-540-28438-9_13
6. A.GelmanJ.B.CarlinH.S.SternD.B.DunsonA.VehtariD.B.Rubin (2013). Bayesian data analysis (3rd ed.). London, England: Chapman & Hall/CRC Press.
7. A.GelmanA.VehtariP.JylänkiC.RobertN.ChopinJ.P.Cunningham. (2014). Expectation propagation as a way of life. arXiv, 1412.4869.
8. Y.GhitzaA.Gelman. (2014). The great society, Reagan’s revolution, and generations of presidential voting. To be submitted.
9. A.GriewankA.Walther (2008). Evaluating derivatives: Principles and techniques of algorithmic differentiation (2nd ed.). Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
10. M.D.HoffmanA.Gelman (2014). The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15, 1593–1623. Retrieved fromhttp://jmlr.org/papers/v15/hoffman14a.html
11. A.KucukelbirR.RanganathA.GelmanD.M.Blei. (2015). Automatic variational inference in Stan. Neural Information Processing Systems, 2015. [arXiv 1506.03431]
12. D.LewandowskiD.KurowickaH.Joe (2009). Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis, 100, 1989–2001.
13. D.LunnD.SpiegelhalterA.ThomasN.Best (2009). The BUGS project: Evolution, critique and future directions. Statistics in Medicine, 28, 3049–3067.
14. D.LunnA.ThomasN.BestD.Spiegelhalter (2000). Winbugs—A Bayesian modeling framework: Concepts, structure, and extensibility. Statistics and Computing, 10, 325–337.
15. A.D.MartinK.M.QuinnJ.H.Park (2011). MCMCpack: Markov chain Monte Carlo in R. Journal of Statistical Software, 42, 22. Retrieved fromhttp://www.jstatsoft.org/v42/i09/
16. N.MetropolisS.Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 335–341.
17. L.MuthénB.Muthén. (1998–2011). Mplus user’s guide (6th ed.) [Computer software manual]. Los Angeles, CA: Author.
18. R.Neal. (2011). MCMC using Hamiltonian dynamics. In S.BrooksA.GelmanG.L.JonesX.-L.Meng (Eds.), Handbook of Markov chain Monte Carlo (pp. 116–162). Chapman and Hall/CRC, London.
19. A.PatilD.HuardC.J.Fonnesbeck (2010). PyMC: Bayesian stochastic modelling in Python. Journal of Statistical Software, 35, 1–81.
20. M.Plummer (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing (Vol. 124, p. 125). Technische Universität Wien, Vienna, Austria.
21. S.Rabe-HeskethA.SkrondalA.Pickles (2005). Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128, 301–323.
22. S.RaudenbushA.BrykR.Congdon (2004). HLM 6 for windows[Computer software manual]. Skokie, IL: Software International.
23. Stan Development Team. (2015). Stan modeling language users guide and reference manual, version 2.6.0[Computer software manual]. Retrieved fromhttp://mc-stan.org/
24. J.VanhataloJ.RiihimäkiJ.HartikainenP.JylänkiV.TolvanenA.Vehtari (2013). GPstuff: Bayesian modeling with Gaussian proceesses. Journal of Machine Learning Research, 14, 1175–1179.