References
- E. Blanchard, A. Sandu, and C. Sandu, A polynomial-chaos-based Bayesian approach for estimating uncertain parameters of mechanical systems, 19th International Conference on Design Theory and Methodology; 1st International Conference on Micro- and Nanosystems; and 9th International Conference on Advanced Vehicle Tire Technologies, Parts A and B; Vol. 3, Las Vegas, NV, 2008, pp. 1041–1048.
- J. Breidt, T. Butler, and D. Estep, A measure-theoretic computational method for inverse sensitivity problems I: Method and analysis, SIAM J. Numer. Anal. 49 (2011), pp. 1836–1859. doi: 10.1137/100785946
- A.O. Cai, K.A. Landman and B.D. Hughes, Multi-scale modeling of a wound-healing cell migration assay, J. Theor. Biol. 245 (2007), pp. 576–594. doi: 10.1016/j.jtbi.2006.10.024
- R. Cameron and W. Martin, The orthogonal development of nonlinear functionals in series of Fourier–Hermite functionals, Ann. Math. 48 (1947), pp. 385–392. doi: 10.2307/1969178
- B.M. Chen-Charpentier and D. Stanescu, Biofilm growth on medical implants with randomness, Math. Comput. Modell. 54 (2011), pp. 1682–1686. doi: 10.1016/j.mcm.2010.11.075
- F. Coelho, C. Torres, and M.G.M. Gomes, A Bayesian framework for parameter estimation in dynamical models, PLoS ONE 6(5) (2011), e19616, pp. 1–6.
- R. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Dover Publications, Mineola, NY, 1991. doi: 10.1007/978-1-4612-3094-6
- G. Kallianpur, Stochastic Filtering Theory, Springer, Berlin, 1980.
- Ch.L. Lawson and R.J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974.
- Y.M. Marzouk and Xiu, A stochastic collocation approach to Bayesian inference in inverse problems, Commun. Comput. Phys. 6(4) (2009), pp. 826–847. doi: 10.4208/cicp.2009.v6.p826
- N. Metropolis and S. Ulam, The Monte Carlo method, J. Am. Stat. Assoc. 44 (1949), pp. 335–341. doi: 10.1080/01621459.1949.10483310
- B.L. Pence, H.K. Fathy, and J.L. Stein, A Maximum likelihood to recursive polynomial chaos parameter estimation, 2010 American Control Conference, Baltimore, MD, USA, 30 June–2 July 2010, pp. 2144–2151.
- F. Perrin, B. Sudret, and M. Pendola, Use of polynomial chaos expansions in stochastic inverse problems, Proceedings 4th Int. ASRANet Colloquium, Athens, Greece, 2008, pp. 1–8.
- S. Ross, A First Course in Probability, Prentice-Hall, Upper Saddle River, NJ, 2002.
- D. Stanescu and B. Chen-Charpentier, Random coefficient differential equation models for bacterial growth, Math. Comput. Modell. 50 (2009), pp. 885–895. doi: 10.1016/j.mcm.2009.05.017
- A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA, 2005.
- R.W. Walters and L. Huyse, Uncertainty quantification for fluid mechanics with applications, ICASE Report No. 2002-1, NASA Langley Research Center, Hampton, VA, 2002.
- M. Wand and M. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.
- N. Wiener, The homogeneous chaos, Am. J. Math. 60 (1938), pp. 897–936. doi: 10.2307/2371268
- D. Xiu and G.E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput. 24 (2002), pp. 619–664. doi: 10.1137/S1064827501387826