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Describes computational methods for parametric and nonparametric modeling of stochastic dynamics. Aimed at graduate students, and suitable for self-study.
List of contents
1. Introduction; 2. Markov chain Monte Carlo; 3. Ensemble Kalman filters; 4. Stochastic spectral methods; 5. Karhunen-Loève expansion; 6. Diffusion forecast; Appendix A. Elementary probability theory; Appendix B. Stochastic processes; Appendix C. Elementary differential geometry; References; Index.
About the author
John Harlim is a Professor of Mathematics and Meteorology at the Pennsylvania State University. His research interests include data assimilation and stochastic computational methods. In 2012, he received the Frontiers in Computational Physics award from the Journal of Computational Physics for his research contributions on computational methods for modeling Earth systems. He has previously co-authored another book, Filtering Complex Turbulent Systems (Cambridge, 2012).
Summary
The mathematics behind, and the practice of, computational methods that leverage data for modelling dynamical systems are described in this book. It will teach readers how to fit data on the assumed model and how to use data to determine the underlying model. Suitable for graduate students in applied mathematics, statistics, and engineering.
