References

Transport Map

[TM1]Tarek a. El Moselhy and Youssef M. Marzouk. Bayesian inference with optimal maps. Journal of Computational Physics, 231(23):7815–7850, oct 2012. doi:10.1016/j.jcp.2012.07.022.
[TM2]Youssef Marzouk, Tarek Moselhy, Matthew Parno, and Alessio Spantini. Sampling via Measure Transport: An Introduction. In Roger G. Ghanem, David Higdon, and Houman Owhadi, editors, Handbook of Uncertainty Quantification, pages 1–41. Springer International Publishing, Cham, 2016. arXiv:1602.05023, doi:10.1007/978-3-319-11259-6_23-1.
[TM3]Matthew Parno and Youssef Marzouk. Transport map accelerated Markov chain Monte Carlo. submitted, pages 1–50, 2014. arXiv:1412.5492v2.
[TM4]Alessio Spantini, Daniele Bigoni, and Youssef Marzouk. Inference via low-dimensional couplings. preprint, 2017. arXiv:1703.06131.
[TM5]Rebecca Morrison, Ricardo Baptista, and Youssef Marzouk. Beyond normality: learning sparse probabilistic graphical models in the non-gaussian setting. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems 30, pages 2359–2369. Curran Associates, Inc., 2017. URL: http://papers.nips.cc/paper/6830-beyond-normality-learning-sparse-probabilistic-graphical-models-in-the-non-gaussian-setting.pdf.

Other References

[OR1]Cédric Villani. Optimal Transport. Volume 338 of Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009. ISBN 978-3-540-71049-3. URL: http://link.springer.com/10.1007/978-3-540-71050-9, doi:10.1007/978-3-540-71050-9.
[OR2]V I Bogachev, A V Kolesnikov, and K V Medvedev. Triangular transformations of measures. Sbornik: Mathematics, 196(3):309–335, 2005. doi:10.1070/SM2005v196n03ABEH000882.
[OR3]Herbert Knothe. Contributions to the Theory of Convex Bodies. The Michigan Mathematical Journal, 4(1):39–52, 1957. doi:10.1307/mmj/1028990175.
[OR4]Murray Rosenblatt. Remarks on a Multivariate Transformation. The Annals of Mathematical Statistics, 23(3):470–472, 1952. doi:10.1214/aoms/1177729394.
[OR5]Annett B. Sullivan, Dean M. Snyder, and Stewart A. Rounds. Controls on biochemical oxygen demand in the upper Klamath River, Oregon. Chemical Geology, 269(1-2):12–21, 2010. doi:10.1016/j.chemgeo.2009.08.007.
[OR6]Christian P. Robert and George Casella. Monte Carlo Statistical Methods. Volume 1 of Springer Texts in Statistics. Springer New York, New York, NY, 2004. ISBN 978-1-4419-1939-7. doi:10.1007/978-1-4757-4145-2.
[OR7]John Hull and Alan White. The Pricing of Options on Assets with Stochastic Volatilities. The Journal of Finance, 42(2):281–300, jun 1987. doi:10.1111/j.1540-6261.1987.tb02568.x.
[OR8]Sangjoon Kim, Neil Shephard, and Siddhartha Chib. Stochastic volatility: likelihood inference and comparison with ARCH models. The Review of Economic Studies, 65(December 1994):361–393, 1998. doi:10.1111/1467-937X.00050.
[OR9]Steffen L. Lauritzen. Graphical Models. Graphical Models, 1996.
[OR10]Robert Grover Brown and Patrick Y. C. Hwang. Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions. John Wiley & Sons, Inc., 3rd edition, 1997.
[OR11]B. E. Bona and Robert J. Smay. Optimum Reset of Ship’s Inertial Navigation System. IEEE Transactions on Aerospace and Electronic Systems, AES-2(4):409–414, 1966. doi:10.1109/TAES.1966.4501790.
[OR12]R E Kalman. A New Approach to Linear Filtering and Prediction Problems 1. Journal of Fluids Engineering, 82(Series D):35–45, 1960. doi:10.1115/1.3662552.
[OR13]J. Durbin and S. J. Koopman. Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(1):3–56, feb 2000. doi:10.1111/1467-9868.00218.
[OR14]Håvard Rue, Sara Martino, and Nicolas Chopin. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2):319–392, apr 2009. doi:10.1111/j.1467-9868.2008.00700.x.