Stan : A Probabilistic Programming Language

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; Lee, Daniel; Goodrich, Ben; Betancourt, Michael; Brubaker, Marcus; Guo, Jiqiang; Li, Peter; Riddell, Allen

doi:10.18637/jss.v076.i01

Stan : A Probabilistic Programming Language

Journal Article · Sun Jan 01 00:00:00 EST 2017 · Journal of Statistical Software

DOI:https://doi.org/10.18637/jss.v076.i01· OSTI ID:1430202

Carpenter, Bob ^[1]; Gelman, Andrew ^[2]; Hoffman, Matthew D. ^[3]; Lee, Daniel ^[2]; Goodrich, Ben ^[2]; Betancourt, Michael ^[2]; Brubaker, Marcus ^[4]; Guo, Jiqiang ^[5]; Li, Peter ^[2]; Riddell, Allen ^[6]

Columbia Univ., New York, NY (United States); None
Columbia Univ., New York, NY (United States)
Adobe Creative Intelligence Lab, San Jose, CA (United States)
York Univ., Toronto (Canada)
NPD Group, Inc., Port Washington, NY (United States)
Indiana Univ., Bloomington, IN (United States)

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.

View Accepted Manuscript (DOE)

Research Organization:: Columbia Univ., New York, NY (United States); Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: National Inst. of Health (NIH); National Science Foundation (NSF); US Dept. of Education, Inst. of Education Sciences (IES); USDOE

Grant/Contract Number:: SC0002099

OSTI ID:: 1430202

Journal Information:: Journal of Statistical Software, Journal Name: Journal of Statistical Software Journal Issue: 1 Vol. 76; ISSN JSSOBK; ISSN 1548-7660

Country of Publication:: United States

Language:: English

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Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics Fourment, Mathieu; Darling, Aaron E. PeerJ https://doi.org/10.1101/702944	journal	July 2019
Indication of a reduction in the cover of thin-leaved plants in Danish grasslands over an eight-year period Damgaard, Christian bioRxiv https://doi.org/10.1101/735472	posted_content	January 2020
Reconstruction of plant–pollinator networks from observational data Young, Jean-Gabriel; Valdovinos, Fernanda S.; Newman, M. E. J. https://doi.org/10.1101/754077	posted_content	June 2021
Anxious and obsessive-compulsive traits are independently associated with valuation of non-instrumental information Bennett, Daniel; Sutcliffe, Kiran; Tan, Nicholas Poh-Jie Journal of Experimental Psychology: General https://doi.org/10.1101/768168	journal	May 2020
A sub-exponential branching process to study early epidemic dynamics with application to Ebola Zarebski, Alexander E.; Moss, Robert; McCaw, James M. https://doi.org/10.1101/797878	posted_content	October 2019
Tunings for leapfrog integration of Hamiltonian Monte Carlo for estimating genetic parameters Arakawa, Aisaku; Hayashi, Takeshi; Taniguchi, Masaaki BioRxiv https://doi.org/10.1101/805499	posted_content	October 2019
Testing Darwin’s naturalization conundrum based on taxonomic, phylogenetic and functional dimensions of vascular plants Pinto-Ledezma, Jesús N.; Villalobos, Fabricio; Reich, Peter B. Ecological Monographs https://doi.org/10.1101/847442	journal	November 2019
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Studying strong phase transitions in neutron stars with gravitational waves Chatziioannou, Katerina; Han, Sophia Physical Review D, Vol. 101, Issue 4 https://doi.org/10.1103/physrevd.101.044019	journal	February 2020
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Indices of Effect Existence and Significance in the Bayesian Framework Makowski, Dominique; Ben-Shachar, Mattan S.; Chen, S. H. Annabel https://doi.org/10.31234/osf.io/2zexr	preprint	December 2019
A Psychometrics of Individual Differences in Experimental Tasks Rouder, Jeffrey N.; Haaf, Julia M. PsyArXiv Preprints https://doi.org/10.31234/osf.io/f3h2k	posted_content	August 2018
Debiasing in a minute or less, or too good to be true? The effect of micro-interventions on decision-making quality Kovic, Marko https://doi.org/10.31235/osf.io/c3udt	preprint	December 2018
X vs. Y: An Analysis of Intergenerational Differences in Transport Mode Use Among Young Adults Kruger, Rico; Rashidi, Taha H.; Vij, Akshay SocArXiv Papers https://doi.org/10.31235/osf.io/unezy	posted_content	December 2018
Accounting for Bacterial Overlap Between Raw Water Communities and Contaminating Sources Improves the Accuracy of Signature-Based Microbial Source Tracking Hägglund, Moa; Bäckman, Stina; Macellaro, Anna Frontiers in Microbiology, Vol. 9 https://doi.org/10.3389/fmicb.2018.02364	journal	October 2018
Local Fields in Human Subthalamic Nucleus Track the Lead-up to Impulsive Choices Pearson, John M.; Hickey, Patrick T.; Lad, Shivanand P. Frontiers in Neuroscience, Vol. 11 https://doi.org/10.3389/fnins.2017.00646	journal	November 2017
Visual Iconicity Across Sign Languages: Large-Scale Automated Video Analysis of Iconic Articulators and Locations Östling, Robert; Börstell, Carl; Courtaux, Servane Frontiers in Psychology, Vol. 9 https://doi.org/10.3389/fpsyg.2018.00725	journal	May 2018
Social Influence in Adolescent Decision-Making: A Formal Framework Ciranka, Simon; van den Bos, Wouter Frontiers in Psychology, Vol. 10 https://doi.org/10.3389/fpsyg.2019.01915	journal	August 2019
“We Wait”—The Impact of Character Responsiveness and Self Embodiment on Presence and Interest in an Immersive News Experience Steed, Anthony; Pan, Ye; Watson, Zillah Frontiers in Robotics and AI, Vol. 5 https://doi.org/10.3389/frobt.2018.00112	journal	October 2018
Multi-Model Forecasts of Very-Large Fire Occurences during the End of the 21st Century Podschwit, Harry; Larkin, Narasimhan; Steel, E. Climate, Vol. 6, Issue 4 https://doi.org/10.3390/cli6040100	journal	December 2018
Bayesian Calibration with Augmented Stochastic State-Space Models of District-Heated Multifamily Buildings Lundström, Lukas; Akander, Jan Energies, Vol. 13, Issue 1 https://doi.org/10.3390/en13010076	journal	December 2019
Effect of Training Load on Post-Exercise Cardiac Troponin T Elevations in Young Soccer Players Cirer-Sastre, Rafel; Legaz-Arrese, Alejandro; Corbi, Francisco International Journal of Environmental Research and Public Health, Vol. 16, Issue 23 https://doi.org/10.3390/ijerph16234853	journal	December 2019
Spotted Wing Drosophila in Sweet Cherry Orchards in Relation to Forest Characteristics, Bycatch, and Resource Availability Hennig, Ernest; Mazzi, Dominique Insects, Vol. 9, Issue 3 https://doi.org/10.3390/insects9030118	journal	September 2018
Evaluating the Within-Host Dynamics of Ranavirus Infection with Mechanistic Disease Models and Experimental Data Mihaljevic, Joseph R.; Greer, Amy L.; Brunner, Jesse L. Viruses, Vol. 11, Issue 5 https://doi.org/10.3390/v11050396	journal	April 2019
Context effects on reproduced magnitudes from short-term and long-term memory Wedell, Douglas H.; Hayes, William M.; Kim, Jongwan Attention, Perception, & Psychophysics, Vol. 82, Issue 4 https://doi.org/10.3758/s13414-019-01932-z	journal	January 2020
Time-conjunctive representations of future events Babcock, Stuart W.; Howard, Marc W.; McGuire, Joseph T. Memory & Cognition, Vol. 48, Issue 4 https://doi.org/10.3758/s13421-019-00999-1	journal	December 2019
The relative merit of empirical priors in non-identifiable and sloppy models: Applications to models of learning and decision-making: Empirical priors Spektor, Mikhail S.; Kellen, David Psychonomic Bulletin & Review, Vol. 25, Issue 6 https://doi.org/10.3758/s13423-018-1446-5	journal	March 2018
Maximum Entropy-based Probabilistic Mass–Radius Relation of Exoplanets Ma, Qi; Ghosh, Sujit K. The Astronomical Journal, Vol. 158, Issue 2 https://doi.org/10.3847/1538-3881/ab2990	journal	July 2019
Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole Witzel, G.; Martinez, G.; Hora, J. The Astrophysical Journal, Vol. 863, Issue 1 https://doi.org/10.3847/1538-4357/aace62	journal	August 2018
The Carnegie Supernova Project: Absolute Calibration and the Hubble Constant Burns, Christopher R.; Parent, Emilie; Phillips, M. M. The Astrophysical Journal, Vol. 869, Issue 1 https://doi.org/10.3847/1538-4357/aae51c	journal	December 2018
`Stingray` : A Modern `Python` Library for Spectral Timing Huppenkothen, Daniela; Bachetti, Matteo; Stevens, Abigail L. The Astrophysical Journal, Vol. 881, Issue 1 https://doi.org/10.3847/1538-4357/ab258d	journal	August 2019
Spectroscopy of the Young Stellar Association Price-Whelan 1: Origin in the Magellanic Leading Arm and Constraints on the Milky Way Hot Halo Nidever, David L.; Price-Whelan, Adrian M.; Choi, Yumi The Astrophysical Journal, Vol. 887, Issue 2 https://doi.org/10.3847/1538-4357/ab52fc	journal	December 2019
A Future Percent-level Measurement of the Hubble Expansion at Redshift 0.8 with Advanced LIGO Farr, Will M.; Fishbach, Maya; Ye, Jiani The Astrophysical Journal, Vol. 883, Issue 2 https://doi.org/10.3847/2041-8213/ab4284	journal	October 2019
Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models McParland, Damien; Baron, Szymon; O'Rourke, Sarah arXiv https://doi.org/10.48550/arxiv.1608.03091	preprint	January 2016
Robust Bayesian Model Selection for Variable Clustering with the Gaussian Graphical Model Andrade, Daniel; Takeda, Akiko; Fukumizu, Kenji arXiv https://doi.org/10.48550/arxiv.1806.05924	preprint	January 2018
Gender Bias in Nobel Prizes Lunnemann, Per; Jensen, Mogens H.; Jauffred, Liselotte arXiv https://doi.org/10.48550/arxiv.1810.07280	preprint	January 2018
Impact of using the ultra-high-energy cosmic ray arrival energies to constrain source associations Capel, Francesca; Mortlock, Daniel J. arXiv https://doi.org/10.48550/arxiv.1811.06464	text	January 2018
Choosing priors in bayesian measurement invariance modeling: A Monte Carlo Simulation study Pokropek, Artur; Schmidt, Peter; Davidov, Eldad Taylor & Francis https://doi.org/10.5167/uzh-182461	text	January 2020
Optimization of process models for determining volatility distribution and viscosity of organic aerosols from isothermal particle evaporation data Tikkanen, Olli-Pekka; Hämäläinen, Väinö; Rovelli, Grazia Atmospheric Chemistry and Physics, Vol. 19, Issue 14 https://doi.org/10.5194/acp-19-9333-2019	journal	January 2019
Probabilistic reanalysis of storm surge extremes in Europe Mir Calafat, Francisco; Marcos, Marta EGU General Assembly 2020 https://doi.org/10.5194/egusphere-egu2020-4888	posted_content	May 2020
Estimating parameter values of a socio-hydrological flood model Barendrecht, Marlies Holkje; Viglione, Alberto; Kreibich, Heidi Proceedings of the International Association of Hydrological Sciences, Vol. 379 https://doi.org/10.5194/piahs-379-193-2018	journal	January 2018
A Bayesian K-PD model for synergy: a case study Gamba, Fabiola La; Jacobs, Tom; Geys, Helena Zenodo https://doi.org/10.5281/zenodo.2562052	text	January 2018
A model for longitudinal data sets relating wind-damage probability to biotic and abiotic factors: a Bayesian approach Umeki, Kiyoshi; Abrams, Marc David; Toyama, Keisuke Forest Systems, Vol. 28, Issue 3 https://doi.org/10.5424/fs/2019283-15200	journal	November 2019
The Blessings of Multiple Causes Wang, Yixin; Blei, David M. Taylor & Francis https://doi.org/10.6084/m9.figshare.10115891.v2	text	January 2020
On the Use of Mixed Markov Models for Intensive Longitudinal Data Haan-Rietdijk, S. De; Kuppens, P.; Bergeman, C. S. Taylor & Francis https://doi.org/10.6084/m9.figshare.5450968	text	January 2017
A New Model for Acquiescence at the Interface of Psychometrics and Cognitive Psychology Plieninger, Hansjörg; Heck, Daniel W. Figshare https://doi.org/10.6084/m9.figshare.6387803.v1	text	January 2018
The Impact of Moderate Priors For Bayesian Estimation and Testing of Item Factor Analysis Models When Maximum Likelihood is Unsuitable Bainter, Sierra A.; Forster, Daniel E. Taylor & Francis https://doi.org/10.6084/m9.figshare.6960449	text	January 2018
The Impact of Moderate Priors For Bayesian Estimation and Testing of Item Factor Analysis Models When Maximum Likelihood is Unsuitable Bainter, Sierra A.; Forster, Daniel E. Taylor & Francis https://doi.org/10.6084/m9.figshare.6960449.v1	text	January 2018
Cadmium in New Zealand agricultural soils Abraham, Edward Taylor & Francis https://doi.org/10.6084/m9.figshare.7496780	text	January 2018
Cadmium in New Zealand agricultural soils Abraham, Edward Taylor & Francis https://doi.org/10.6084/m9.figshare.7496780.v1	text	January 2018
Antecedent access mechanisms in pronoun processing: evidence from the N400 Lago, Sol; Namyst, Anna; Jäger, Lena A. Figshare https://doi.org/10.6084/m9.figshare.7713056	text	January 2019
The effects of syntactic pressures and pragmatic considerations on predictive dependency formation Keshev, Maayan; Meltzer-Asscher, Aya Taylor & Francis https://doi.org/10.6084/m9.figshare.9247637.v1	text	January 2019
Forecasting at Scale Taylor, Sean J.; Letham, Benjamin Peer J Preprints https://doi.org/10.7287/peerj.preprints.3190v1	posted_content	August 2017
DeepPoseKit, a software toolkit for fast and robust animal pose estimation using deep learning Graving, Jacob M.; Chae, Daniel; Naik, Hemal eLife, Vol. 8 https://doi.org/10.7554/eLife.47994	journal	October 2019
Humans treat unreliable filled-in percepts as more real than veridical ones Ehinger, Benedikt V.; Häusser, Katja; Ossandón, José P. eLife, Vol. 6 https://doi.org/10.7554/elife.21761	journal	May 2017
Associability-modulated loss learning is increased in posttraumatic stress disorder Brown, Vanessa M.; Zhu, Lusha; Wang, John M. eLife, Vol. 7 https://doi.org/10.7554/elife.30150	journal	January 2018
MERS-CoV spillover at the camel-human interface Dudas, Gytis; Carvalho, Luiz Max; Rambaut, Andrew eLife, Vol. 7 https://doi.org/10.7554/elife.31257	journal	January 2018
Time preferences are reliable across time-horizons and verbal versus experiential tasks Lukinova, Evgeniya; Wang, Yuyue; Lehrer, Steven F. eLife, Vol. 8 https://doi.org/10.7554/elife.39656	journal	February 2019
Reward prediction error does not explain movement selectivity in DMS-projecting dopamine neurons Lee, Rachel S.; Mattar, Marcelo G.; Parker, Nathan F. eLife, Vol. 8 https://doi.org/10.7554/elife.42992	journal	April 2019
Neural mediation of greed personality trait on economic risk-taking Li, Weiwei; Wang, Haixia; Xie, Xiaofei eLife, Vol. 8 https://doi.org/10.7554/elife.45093	journal	April 2019
Hierarchical generalized additive models in ecology: an introduction with mgcv Pedersen, Eric J.; Miller, David L.; Simpson, Gavin L. PeerJ, Vol. 7 https://doi.org/10.7717/peerj.6876	journal	January 2019
Peer effects on control-averse behavior Rudorf, Sarah; Baumgartner, Thomas; Knoch, Daria Nature Publishing Group https://doi.org/10.7892/boris.128808	text	January 2019

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