Title: Bayesian Calibration of Computationally Expensive Models Using Optimization and Radial Basis Function Approximation
Authors: Nikolai Blizniouk, David Ruppert, Christine Shoemaker, Rommel Regis, Stefan Wild, Pradeep Mugunthan
Abstract: We present a Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given data vector Y corresponding to the regression model f(beta), find plausible values of beta. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of beta given Y using MCMC. To reduce computational cost, we limit evaluation of f to a small number of points chosen on a high posterior density region found by optimization. Then, we approximate the log-posterior using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC. We illustrate our approach on simulated data for a pollutant diffusion problem and study frequentist coverage properties of credible intervals. Our experiments indicate that our method can produce results similar to those when the true "expensive" posterior is sampled by MCMC while reducing computational costs by well over an order of magnitude.
Keywords: Computer Experiments, Design of Experiments, Interpolation, Inverse Problems, Markov Chain Monte Carlo, RBF, Transformation
Thanks: The research of Blizniouk was supported by the National Science Foundation under grant DMS-04-538 (PI's Ruppert and Shoemaker). Research of Wild was supported by a Department of Energy Computational Science Graduate Fellowship, grant number DE-FG0297ER25308. Regis was supported by NSF grant CCF-0305583 (PI Shoemaker) and Mugunthan on NSF grant BES-0229176 (PI Shoemaker). Ruppert and Shoemaker were also partially supported on the grants on which they are PI's.
Status: Appears in Journal of Computational and Graphical Statistics, Vol. 17 (2), pp. 1--25, 2008.
Replaces ORIE Technical Report, September 29, 2006.
Link: [DOI: 10.1198/106186008X320681], [Tech Report PDF]
BibTeX:
@article{BLIZNYUK08,
    author      = "Nikolay Bliznyuk and David Ruppert and Christine A. Shoemaker 
                   and Rommel G. Regis and Stefan M. Wild and Pradeep Mugunthan",
    title       = "Bayesian Calibration of Computationally Expensive Models Using 
                   Optimization and Radial Basis Function Approximation",
    journal     = "Journal of Computational and Graphical Statistics", 
    volume      = "17",    
    year        = "2008",
    number      = "2",
    pages       = "1--25",
    doi         = "10.1198/106186008X320681"
}
	
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