Tutorial I
Files for the first task described in .pdf file you may find in zip file
Files for the second task you may find in zip file
Literature for SAMM 2017
[1] Ivo Babuˇska, Fabio Nobile, and Raul Tempone. "A stochastic collocation method for elliptic partial differential equations with random input data". In: SIAM Journal on Numerical Analysis 45.3 (2007), pp. 1005-1034.
[2] John D Jakeman and Timothy Wildey. "Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates". In: Journal of Computational Physics 280 (2015), pp. 54-71.
[3] O. Le Maˆıtre and Knio O.M. Spectral Methods for Uncertainty Quantification. Springer Science+Business Media B.V. 2010, 2010.
[4] Akil Narayan and John D Jakeman. "Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation". In: SIAM Journal on Scientific Computing 36.6 (2014), A2952-A2983.
[5] Dongbin Xiu and Jan S Hesthaven. "High-order collocation methods for differential equations with random inputs". In:SIAM Journal on Scientific Computing 27.3 (2005), pp. 1118-1139
[6] Hermann G. Matthies, Andreas Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, CMAME 194 (2005) 1295-1331.
[7] Hermann G. Matthies, Stochastic Finite Elements: Computational Approaches to Stochastic Partial Differential Equations, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 88 (11): 849-873, 2008
[8] Christian Soize. Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2006, 195 (1-3), pp.26-64.
[9] H. G. Matthies, E. Zander,B. Rosic and A. Litvinenko. Parameter Estimation via Conditional Expectation - A Bayesian Inversion,
Advanced Modeling and Simulation in Engineering Sciences, available online, 2016
[10] B. Rosic, A. Litvinenko, O. Pajonk and H. G. Matthies. Sampling Free Bayesian Update of Polynomial Chaos Representations. Journal of Computational Physics, 231 (17): 5761-5787, 2012
[11] O. Pajonk, B. Rosic, and H. G. Matthies. Sampling-free Linear Bayesian Updating of Model State and Parameters Using a Square Root Approach. Computers and Geosciences, 2013, 55:70-83
[12] Dashti M and Stuart A M. The Bayesian Approach to Inverse Problems. Handbook of Uncertainty Quantification, Editors R. Ghanem, D. Higdon and H. Owhadi, Springer, 2015.
[13] Kaipio J and Somersalo E, Statistical and Computational Inverse Problems, Springer.
[14] Stuart A M. Inverse problems: a Bayesian perspective. Acta Numerica 19(2010). [15] Cotter S, Dashti M and Stuart A M 2012 Variational data assimilation using targetted random walks, International Journal for Numerical Methods in Fluids, 68. [16] Robert C and Casella G, Monte Carlo Statistical Methods, Springer, 1999. [17] Scheichl R, Stuart A M and Teckentrup A 2016 Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems arXiv preprint arXiv:1602.04704. [18] Schillings C and Schwab C 2014 Sparsity in Bayesian inversion of parametric operator equations Inverse Problems 29 (2013) 065011. [19] Schillings C and Schwab C 2016 Scaling limits in computational Bayesian inversion M2AN