Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations

Computer Methods in Applied Mechanics and Engineering

Volumn 259, Issue , 2013, Pages 24-39

  Long, Quan ^a,b   Scavino, Marco ^a,d   Tempone, Raúl ^a   Wang, Suojin ^c  

^a KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c TEXAS A AND M UNIVERSITY   (United States)

^d UNIVERSIDAD DE LA REPÚBLICA   (Uruguay)

Author keywords

Bayesian experimental design; Bayesian statistics; Information gain; Laplace approximation; Monte Carlo sampling; Sparse quadrature; Uncertainty quantification

Indexed keywords

BAYESIAN EXPERIMENTAL DESIGNS; BAYESIAN STATISTICS; INFORMATION GAIN; LAPLACE APPROXIMATION; MONTE CARLO SAMPLING; SPARSE QUADRATURE; UNCERTAINTY QUANTIFICATIONS;

DESIGN OF EXPERIMENTS; ESTIMATION; EXPERIMENTS; INTEGRATION; LAPLACE TRANSFORMS; MODELS; MONTE CARLO METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION; STATISTICS;

PARAMETER ESTIMATION;

EID: 84876305657     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2013.02.017     Document Type: Article

References (42)

1. Box G.E.P., Lucas H.L. Design of experiments in non-linear situations. Biometrika 1959, 46:77-90.
2. Ford I., Titterington D.M., Kitsos C.P. Recent advances in nonlinear experimental design. Technometrics 1989, 31:49-60.
3. Atkinson A.C., Donev A.N., Tobias R.D. Optimum Experimental Designs, with SAS 2007, Oxford University Press.
4. Chaloner K., Verdinelli I. Bayesian experimental design: a review. Stat. Sci. 1995, 10:273-304.
5. Dette H. A note on Bayesian C- and D-optimal designs in nonlinear regression models. Ann. Stat. 1996, 24:1225-1234.
6. Clyde M., Chaloner K. The equivalence of constrained and weighted designs in multiple objective design problems. J. Am. Stat. Assoc. 1996, 91:1236-1244.
7. Verdinelli I. A note on Bayesian design for the normal linear model with unknown error variance. Biometrika 2000, 87:222-227.
8. Pukelsheim F. Optimal Design of Experiments 2006, SIAM.
9. Kullback S., Leibler R.A. On information and sufficiency. Ann. Math. Stat. 1951, 22:79-86.
10. Kullback S. Information Theory and Statistics 1959, Wiley.
11. Burnham K.P., Anderson D.R. Model Selection and Multimodel Inference 2002, Springer. Second ed.
12. Chen M.H., Shao Q.M., Ibrahim J.G. Monte Carlo Methods in Bayesian Computations 2000, Springer.
13. Robert C.R. The Bayesian Choice 2007, Springer. Second ed.
14. Stigler S.M. Laplace's 1774 memoir on inverse probability. Stat. Sci. 1986, 1:359-363.
15. Wong R. Asymptotic Approximation of Integrals 2001, SIAM.
16. Evans M., Swartz T. Approximating Integrals via Monte Carlo and Deterministic Methods 2000, Oxford University Press.
17. Press S.J. Subjective and Objective Bayesian Statistics 2003, Wiley. Second ed.
18. Tierney L., Kadane J.B. Accurate approximations for posterior moments and marginal densities. J. Am. Stat. Assoc. 1986, 81:82-86.
19. Tierney L., Kass R.E., Kadane J.B. Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Am. Stat. Assoc. 1989, 84:710-716.
20. R.E. Kass, L. Tierney, J.B. Kadane, The validity of posterior expansions based on Laplace's method, in: S. Geisser, J.S. Hodges, S.J. Press, A. Zellner (Eds.), Essays in Honor of George Barnard, North-Holland, Amsterdam, 1990, pp. 473-488.
21. Kass R.E., Tierney L., Kadane J.B. Laplace's method in Bayesian analysis. Contemp. Math. 1991, 115:89-99.
22. Calvetti D., Somersalo E. Introduction to Bayesian Scientific Computing 2007, Springer.
23. Hui I. On sequential designs in nonlinear problems. Biometrika 1998, 85:496-503.
24. Pronzato L. One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal. Metrika 2010, 71:219-238.
25. M.A. Clyde, Bayesian optimal designs for approximate normality, Ph.D. thesis, University of Minnesota, 1993.
26. Ghosh J.K., Delampady M., Samanta T. An Introduction to Bayesian Analysis 2006, Springer.
27. Novak E., Ritter K. The curse of dimension and a universal method for numerical integration. Multivariate Approximation and Splines 1997, 177-188. Birkhäuser, Basel. G. Nürnberger, J.W. Schmidt, G. Walz (Eds.).
28. Nobile F., Tempone R., Webster C.G. A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Numer. Anal. 2008, 46:2309-2345.
29. Bäck J., Nobile F., Tamellini L., Tempone R. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients. Lecture Notes in Computational Science and Engineering 2011, volume 76:43-62. Springer. J.S. Hesthaven, E. Ronquist (Eds.).
30. Beck J., Nobile F., Tamellini L., Tempone R. On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods. Math. Models Meth. Appl. Sci. 2012, 22:1250023-1-1250023-33.
31. Smolyak S.A. Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Math. Dokl. 1963, 4:240-243.
32. Barthelmann V., Novak E., Ritter K. High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 2000, 12:273-288.
33. X. Huan, Y.M. Marzouk, Simulation-based optimal Bayesian experimental design for nonlinear systems, 2011. arxiv:ArXiv:1108.4146v1.
34. Sivia D., Skilling J. Data Analysis: A Bayesian Tutorial 2006, Oxford University Press.
35. Assenheimer M., Laver-Moskovitz O., Malonek D., Manor D., Nahaliel U., Nitzan R., Saad A. The t-scan technology: electrical impedance as a diagnostic tool for breast cancer detection. Physiol. Meas. 2001, 22:1-8.
36. Frerichs I., Scholz J., Weiler N. Electrical impedance tomography and its perspectives in intensive care medicine. Yearbook of Intensive Care and Emergency Medicine 2006, 437-447. Springer Berlin, Heidelberg. J.-L. Vincent (Ed.).
37. Schueler R., Joshi S.P., Schulte K. Damage detection in CFRP by electrical conductivity mapping. Compos. Sci. Technol. 2001, 61:921-930.
38. Kaipio J., Somersalo E. Statistical and Computational Inverse Problems 2004, Springer.
39. Carlsson J., Sandberg M., Szepessy A. Symplectic Pontryagin approximations for optimal design. Math. Model. Numer. Anal. 2009, 43:3-32.
40. Horesh L., Haber E., Tenorio L. Optimal experimental design for the large-scale nonlinear ill-posed problem of impedance imaging. Large-Scale Inverse Problems and Quantification of Uncertainty 2010, 273-290. John Wiley & Sons, Ltd. L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders, K. Willcox (Eds.).
41. Somersalo E., Cheney M., Isaacson D. Existence and uniqueness for electrode models for electric current computed tomography. SIAM J. Appl. Math. 1992, 52:1023-1040.
42. Ryan K.J. Estimating expected information gains for experimental designs with application to the random fatigue-limit model. J. Comput. Graphical Stat. 2003, 12:585-603.