mcmc

A Rust library implementing various MCMC diagnostics and utilities, such as Gelman Rubin potential scale reduction factor (R hat), effective sample size (ESS), chain splitting, and others.

This crate is language agnostic and intended to work with the outputs of any MCMC sampler (e.g. Stan, PyMC3, Turing.jl, etc).

Implementation

Currently we expect plain vectors of f64 floating point numbers, but this may be worth generalizing to f32s as well (see roadmap below).

Implementations for some of these diagnostics vary slightly, so reference implementations are based on Stan, and unit tests are adapted from the Stan codebase to ensure matching behavior.

Roadmap

Diagnostics

• [X] Potential scale reduction factor
• [X] Split potential scale reduction factor
• [X] Effective sample size
• [X] Monte Carlo Standard Error

Utilities

• [X] Split chains as recommended in Vehtari, et al 2019
• [ ] Thinning

Data structures

• [ ] Introduce Num type to generalize our implementations to work for f32 or f64.
• [ ] Would it be helpful to have some kind of struct that can represent one or more sample chains with a parameter name?

Performance

• [ ] Remove unnecessary copying or allocation

References

   Convergence of Iterative Simulations.
   _Journal of Computational and Graphical Statistics_, 7(4), 1998.

   Using Multiple Sequences. _Statistical Science_, 7(4):457-472, 1992.

   Burkner. Rank-normalization, folding, and localization: An improved R-hat
   for assessing convergence of MCMC, 2019. Retrieved from
   [http://arxiv.org/abs/1903.08008]().

   _Handbook of Markov Chain Monte Carlo_, edited by Steve Brooks, Andrew Gelman,
   Galin L. Jones, and Xiao-Li Meng. Chapman; Hall/CRC. 2011.

Acknowledgements

Thanks to Ivan Ukhov for generously providing the mcmc namespace on Cargo.