Asymptotic sampling distribution for polynomial chaos representation of data: A maximum entropy and fisher information approach

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 4139-4144

  Das, Sonjoy ^a,b   Ghanem, Roger ^c   Spall, James C ^d  

^a University of Southern California   (United States)

^b Johns Hopkins University   (United States)

^c UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^d JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY   (United States)

Author keywords

Fisher information matrix; Karhunen Lo ve expansion; Markov chain Monte Carlo; Maximum entropy probability density estimation; Non Gaussian and non stationary non homogeneous random process field; Polynomial chaos expansion

Indexed keywords

DISTRIBUTION FUNCTIONS; FISHER INFORMATION MATRIX; POLYNOMIALS; RANDOM PROCESSES; SET THEORY;

MAXIMUM-ENTROPY PROBABILITY DENSITY ESTIMATION; POLYNOMIAL CHAOS EXPANSION;

ASYMPTOTIC STABILITY;

EID: 39649109867     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377613     Document Type: Conference Paper

References (17)

1. S. Das, R. Ghanem, and J. C. Spall, "Asymptotic sampling distribution for polynomial chaos representation of data : A maximum-entropy and Fisher information approach," SIAM Journal on Scientific Computing, 2006, submitted.
2. D. Xiu and G. E. Karniadakis, "The Wiener-Askey polynomial chaos for stochastic differerntial equations," SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 619-643, 2002.
3. S. Sakamoto and R. Ghanem, "Simulation of multi-dimensional non-Gaussian non-stationary random fields," Probabilistic Engineering Mechanics, vol. 17, no. 2, pp. 167-176, April 2002.
4. C. Soize and R. Ghanem, "Physical systems with random uncertainties: Chaos representations with arbitrary probability measure," SIAM Journal on Scientific Computing, vol. 26, no. 2, pp. 395-410, 2004.
5. R. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, 1991, revised edition published by Dover Publications Inc. in 2003.
6. P. Billingsley, Probability and Measure. John Wiley & Sons, 1995.
7. I. Jolliffe, Principal Component Analysis, 2nd ed. Springer, Oct 2002.
8. M. Srikanth, H. K. Kesavan, and P. H. Roe, "Probability density function estimation using the minmax measure," IEEE Trans. Syst., Man, Cybern. C, vol. 30, no. 1, pp. 77-83, February 2000.
9. J. N. Kapur and H. K. Kesavan, Entropy Optimization Principles with Applications. Academic Press Inc., 1992.
10. M. Rosenblatt, "Remarks on multivariate transformation," The Annals of Mathematical Statistics, vol. 23, no. 3, pp. 470-472, September 1952.
11. C. Descelliers, R. Ghanem, and C. Soize, "Maximum likelihood estimation of stochastic chaos representation from experimental data," International Journal for Numerical Methods in Engineering, vol. 66, no. 6, pp. 978-1001, 2006.
12. G. Casella and R. L. Berger, Statistical Inference. Duxbury, 2002.
13. J. C. Spall, Introduction to Stochastic Search and Optimization: Estimation, Simulation and Control. Wiley-Interscience, 2003.
14. _, "Monte carlo computation of the Fisher information matrix in nonstandard settings," Journal of Computational and Graphical Statistics, vol. 14, no. 4, pp. 889-909, 2005.
15. _, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Automat. Contr., vol. 37, no. 3, pp. 332-341, 1992.
16. K. K. Phoon, S. T. Quek, and H. Huang, "Simulation of non-Gaussian process using fractile correlation," Probabilistic Engineering Mechanics, vol. 19, pp. 287-292, 2004.
17. D. W. Scott, Multivariate Density Estimation: Theory, Practice and Visualization. Wiley-Interscience, Aug 1992.