Implementation of robust dynamic Hamiltonian Monte Carlo methods in Julia.

Project Status: Active – The project has reached a stable, usable state and is being actively developed. build codecov.io Documentation Documentation DOI Aqua QA


This package implements a modern version of the “No-U-turn sampler” in the Julia language, mostly as described in Betancourt (2017), with some tweaks.

In contrast to frameworks which utilize a directed acyclic graph to build a posterior for a Bayesian model from small components, this package requires that you code a log-density function of the posterior in Julia. Derivatives can be provided manually, or using automatic differentiation.

Consequently, this package requires that the user is comfortable with the basics of the theory of Bayesian inference, to the extent of coding a (log) posterior density in Julia. This approach allows the use of standard tools like profiling and benchmarking to optimize its performance.

The building blocks of the algorithm are implemented using a functional (non-modifying) approach whenever possible, allowing extensive unit testing of components, while at the same time also intended to serve as a transparent, pedagogical introduction to the low-level mechanics of current Hamiltonian Monte Carlo samplers, and as a platform for research into MCMC methods.

Please start with the documentation.


Support and participation

For general questions, open an issue or ask on the Discourse forum. I am happy to help with models.

Users who rely on this package and want to participate in discussions are recommended to subscribe to the Github notifications (“watching” the package). Also, I will do my best to accommodate feature requests, just open issues.


Betancourt, M. J., Byrne, S., & Girolami, M. (2014). Optimizing the integrator step size for Hamiltonian Monte Carlo. arXiv preprint arXiv:1411.6669.

Betancourt, M. (2016). Diagnosing suboptimal cotangent disintegrations in Hamiltonian Monte Carlo. arXiv preprint arXiv:1604.00695.

Betancourt, M. (2017). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. : CRC Press.

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models.

Hoffman, M. D., & Gelman, A. (2014). The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593-1623.

McElreath, R. (2018). Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and Hall/CRC.