This repository contains illustrative examples for transport-based Bayesian inference. The content was created by Mathieu Le Provost and Youssef Marzouk (MIT) for the UQ Workshop hosted at the University of Southern California in August, 2023.
We use the library TransportBasedInference.jl (https://github.com/mleprovost/TransportBasedInference.jl) developed in Julia.
[1]: Baptista, R., Zahm, O., & Marzouk, Y. (2020). On the representation and learning of monotone triangular transport maps. arXiv preprint arXiv:2009.10303.
[2]: Le Provost, M., Baptista, R., Marzouk, Y. and Eldredge, J., 2021. A low-rank nonlinear ensemble filter for vortex models of aerodynamic flows. In AIAA Scitech 2021 Forum (p. 1937).
[3]: 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.
[4]: 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.
[5]: Spantini, A., Baptista, R., & Marzouk, Y. (2019). Coupling techniques for nonlinear ensemble filtering. SIAM Review. 2022;64(4):921-53.
[6]: Marzouk, Y., Moselhy, T., Parno, M., & Spantini, A. (2016). Sampling via measure transport: An introduction. Handbook of uncertainty quantification, 1-41.