TransportBasedInference.jl

A Julia package for Bayesian inference with transport maps

The objective of this package is to allow for easy and fast resolution of Bayesian inference problems using transport maps. The package provides tools for:

• joint and conditional density estimation from limited samples of the target distribution using the adaptive transport map algorithm developed by Baptista et al. ¹.
• sequential inference for state-space models using one of the following algorithms: the (localized) stochastic ensemble Kalman filter (Evensen ²), the ensemble transform Kalman filter (Bishop et al. ³) and a nonlinear generalization of the stochastic ensemble Kalman filter (Spantini et al. ⁴).

Installation

TransportBasedInference.jl is registered in the general Julia registry. To install, type e.g.,

] add TransportBasedInference

Then, in any version, type

julia> using TransportBasedInference

Tutorials

For examples, consult the documentation or see the Jupyter notebooks in the examples folder.

References

Footnotes

1. Baptista, R., Zahm, O., & Marzouk, Y. (2020). An adaptive transport framework for joint and conditional density estimation. arXiv preprint arXiv:2009.10303. ↩

2. Evensen, G., 1994. Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research: Oceans, 99(C5), pp.10143-10162. ↩

3. Bishop, C.H., Etherton, B.J. and Majumdar, S.J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), pp.420-436. ↩

4. Spantini, A., Baptista, R., & Marzouk, Y. (2019). Coupling techniques for nonlinear ensemble filtering. arXiv preprint arXiv:1907.00389. ↩